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Tools for Discovering and Characterizing Extrasolar Planets Tools for discovering and characterizing extrasolar planets PhD Dissertation Written by: Andr´as P´al Lorand´ Eotv¨ os¨ University, Faculty of Sciences PhD School of Physics PhD Program of Particle- and Astrophysics Head of PhD School of Physics: Prof. Zal´an Horv´ath Head of the PhD program: Prof. Ferenc Csikor Thesis advisor: Dr. G´asp´ar Bakos, postdoctoral fellow of the National Science Foundation Harvard-Smithsonian Center for Astrophysics Supervisor: Prof. B´alint Erdi,´ professor Department of Astronomy Lor´and E¨otv¨os University Lor´and E¨otv¨os University Budapest, Hungary 2009 Foreword Among the group of extrasolar planets, transiting planets provide a great opportunity to obtain direct measurements for the basic physical properties, such as mass and radius of these objects. These planets are therefore highly important in the understanding of the evolution and formation of planetary systems: from the observations of photometric transits, the interior structure of the planet and atmospheric properties can also be constrained. The most efficient way to search for transiting extrasolar planets is based on wide-field surveys by hunting for short and shallow periodic dips in light curves covering quite long time intervals. These surveys monitor fields with several degrees in diameter and tens or hundreds of thousands of objects simultaneously. In the practice of astronomical observations, surveys of large field-of-view are rather new and therefore require special methods for photometric data reduction that have not been used before. Since 2004, I participate in the HATNet project, one of the leading initiatives in the competitive search for transiting planets. Due to the lack of software solution which is capable to handle and properly reduce the yield of such a wide-field survey, I have started to develop a new package designed to perform the related data processing and analysis. After several years of improvement, the software package became sufficiently robust and played a key role in the discovery of several transiting planets. In addition, various new algorithms for data reduction had to be developed, implemented and tested which were relevant during the reduction and the interpretation of data. In this PhD thesis, I summarize my efforts related to the development of a complete software solution for high precision photometric reduction of astronomical images. I also demonstrate the role of this newly developed package and the related algorithms in the case of particular discoveries of the HATNet project. i ii Contents 1 Introduction 1 2 Algorithms and Software environment 5 2.1 Difficulties with undersampled, crowded and wide-field images ........ 6 2.1.1 Undersampledimages........................... 7 2.1.2 Crowdedimages.............................. 12 2.1.3 Largefield-of-view ............................ 13 2.2 Problems with available software solutions . ......... 16 2.3 Calibrationandmasking . .. 16 2.3.1 Stepsofthecalibrationprocess . ... 17 2.3.2 Masking .................................. 18 2.3.3 Implementation .............................. 19 2.4 Detectionofstars................................ 21 2.4.1 Imagepartitioning ............................ 23 2.4.2 Coordinates, shape parameters and analytic models . ........ 27 2.4.3 Implementation .............................. 31 2.5 Astrometry .................................... 31 2.5.1 Introduction................................ 31 2.5.2 Symmetricpointmatching . 33 2.5.3 Findingthetransformation. .. 34 2.5.4 Implementation .............................. 42 2.6 Registeringimages ............................... 43 2.6.1 Choosingareferenceimage . 44 2.6.2 Relativetransformations . .. 44 2.6.3 Conservingflux .............................. 46 2.6.4 Implementation .............................. 47 iii 2.7 Photometry .................................... 48 2.7.1 Rawinstrumentalmagnitudes . 48 2.7.2 Formalismfortheaperturephotometry . .... 50 2.7.3 Magnitudetransformations. .. 51 2.7.4 Implementation .............................. 52 2.8 Imageconvolutionandsubtraction . ..... 52 2.8.1 Referenceframe.............................. 55 2.8.2 Registration................................ 55 2.8.3 Implementation .............................. 56 2.9 Photometryonsubtractedimages . .... 56 2.10Trendfiltering.................................. 57 2.10.1 BasicequationsfortheEPDandTFA . 60 2.10.2 Reconstructive and simultaneous trend removals . ......... 61 2.10.3 Efficiencyofthesemethods . 63 2.11 Majorconcepts ofthesoftwarepackage . ....... 63 2.11.1 Datastructures .............................. 65 2.11.2 Operatingenvironment . 66 2.12Implementation ................................. 68 2.12.1 Basic operations on FITS headers and keywords – fiheader ..... 70 2.12.2 Basic arithmetic operations on images – fiarith ........... 71 2.12.3 Basic information about images – fiinfo ................ 72 2.12.4 Combination of images – ficombine .................. 72 2.12.5 Calibration of images – ficalib ..................... 73 2.12.6 Rejection and masking of nasty pixels – fiign ............. 73 2.12.7 Generation of artificial images – firandom ............... 74 2.12.8 Detection of stars or point-like sources – fistar ............ 76 2.12.9 Basic coordinate list manipulations – grtrans ............. 76 2.12.10 Matching lists or catalogues – grmatch ................. 77 2.12.11 Transforming and registering images – fitrans ............ 78 2.12.12 Convolution and image subtraction – ficonv .............. 79 2.12.13 Photometry – fiphot ........................... 80 2.12.14 Transposition of tabulated data – grcollect .............. 81 2.12.15 Archiving – fizip and fiunzip ..................... 84 2.12.16 Generic arithmetic evaluation, regression and data analysis – lfit .. 85 iv 2.13 Analysisofphotometricdata. ..... 88 3 HATNet discoveries 93 3.1 Photometricdetection . .. .. .. 93 3.2 Follow-upobservations . ... 97 3.2.1 Reconnaissance spectroscopy . ... 97 3.2.2 Highresolutionspectroscopy. ... 97 3.2.3 Photometric follow-up observations . ..... 98 3.2.4 Excluding blend scenarios . 99 3.3 Analysis ...................................... 100 3.3.1 Independentfits.............................. 101 3.3.2 Joint fit based on the aperture photometry data and the single partial follow-uplightcurve . 105 3.3.3 Joint fit based on the image subtraction photometry data and both of thefollow-uplightcurves. 106 3.3.4 Stellarparameters ............................ 108 3.3.5 Planetaryandorbitalparameters . 109 4 Follow-up observations 111 4.1 Photometric observations and reductions . ........ 112 4.2 Radialvelocityobservations . ..... 115 4.3 An analytical formalism for Kepler’s problem . ......... 116 4.3.1 Mathematicalformalism . 116 4.3.2 Additional constraints given by the transits . ....... 119 4.3.3 Practicalimplementation. 120 4.4 Analysis of the HAT-P-2 planetary system . ...... 121 4.4.1 Light curve and radial velocity parameters . ...... 122 4.4.2 Effects of the orbital eccentricity . .... 123 4.4.3 Jointfit .................................. 125 4.4.4 Stellarparameters ............................ 126 4.4.5 Planetaryparameters. 127 4.4.6 Photometric parameters and the distance of the system ........ 128 4.5 Discussion..................................... 130 5 Summary 133 v vi Chapter 1 Introduction In the last two decades, the discovery and characterization of extrasolar planets became an exciting field of astronomy. The first companion that was thought to be an object roughly 10 times more massive than Earth, had been detected around the pulsar PSR1829-10 (Bailes, Lyne & Shemar, 1991). Although this detection turned out to be a false one (Lyne & Bailes, 1992), shortly after the method of detecting planetary companions involving the analysis of pulsar timing variations led to the successful confirmation of the multiple planetary sys- tem around PSR1257+12 (Wolszczan & Frail, 1992). The pioneering discovery of a planet orbiting a main sequence star was announced by Mayor & Queloz (1995). They reported the presence of a short-period planet orbiting the Sun-like star 51 Peg. This detection was based on precise radial velocity measurements with uncertainties at the level of meter per second. Both discovery methods mentioned above are based on the fact that all components in a single or multiple planetary system, including the host star itself, revolve around the common barycenter, that is the point in the system having inertial motion. Thus, com- panions with smaller masses offset the barycenter only slightly from the host star whose motion is detected, either by the analysis of pulsar timing variations or by radial velocity measurements. Therefore, such methods – which are otherwise fairly common among the investigation techniques of binary or multiple stellar systems – yielded success in the form of confirming planets only after the evolution of instrumentation. Due to the physical con- straints found in these methods, the masses of the planets can only be constrained by a lower limit, while we even do not have any information on the sizes of these objects. The discovery of 51 Peg b was followed by numerous other detections, mainly by the method of radial velocity analysis, yielding the discovery, for instance, of the first planetary system with two planets around 47 UMa (Butler & Marcy, 1996; Fischer et al., 2002), and the first multiple planetary system around υ And (Butler et al., 1999). Until the first photometric detection of planetary transits in the system of HD 209458(b) (Henry et al., 2000; Charbonneau et
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