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Dissertation submitted to the Combined Faculties of the Natural Sciences and Mathematics of the Ruperto-Carola-University of Heidelberg, Germany for the degree of Doctor of Natural Science Put forward by Diplom-Physikerin Eva Meyer born in: Essen, Germany Oral Examination: 21st July 2010 High Precision Astrometry with Adaptive Optics aided Imaging Referees: Prof. Dr. Hans-Walter Rix Prof. Dr. Joachim Wambsganß Abstract Currently more than 450 exoplanets are known and this number increases nearly every day. Only a few constraints on their orbital parameters and physical characteristics can be determined, as most exoplanets are detected indirectly and one should therefore refer to them as exoplanet candidates. Measuring the astrometric signal of a planet or low mass companion by means of measuring the wobble of the host star yields the full set of orbital parameters. With this information the true masses of the planet candidates can be determined, making it possible to establish the candidates as real exoplanets, brown dwarfs or low mass stars. In the context of this thesis, an M-dwarf star with a brown dwarf candidate companion, discovered by radial velocity measurements, was observed within an astrometric monitoring program to detect the astrometric signal. Ground based adaptive optics aided imaging with the ESO/NACO instrument was used with the aim to establish its true nature (brown dwarf vs. star) and to investigate the prospects of this technique for exoplanet detection. The astrometric corrections necessary to perform high precision astrometry are described and their contribution to the overall precision is investigated. Due to large uncertainties in the pixel-scale and the orientation of the detector, no detection of the astrometric orbit signal was possible. The image quality of ground-based telescopes is limited by the turbulence in Earth’s at- mosphere. The induced distortions of the light can be measured and corrected with the adaptive optics technique and nearly diffraction limited performance can be achieved. However, the correction is only useful within a small angle around the guide star in single guide star measurements. The novel correction technique of multi conjugated adaptive optics uses several guide stars to correct a larger field of view. The VLT/MAD instrument was built to demonstrate this technique. Observations with MAD are an- alyzed in terms of astrometric precision in this work. Two sets of data are compared, which were obtained in different correction modes: pure ground layer correction and full multi conjugated correction. i Zusammenfassung Mehr als 450 extrasolare Planeten sind zurzeit bekannt und diese Zahl wird fast t¨aglich gr¨osser.Da die meisten Exoplaneten indirekt entdeckt werden, k¨onnennur wenige Ein- schr¨ankungenbez¨uglich ihrer Bahnparameter und physikalischen Eigenschaften gemacht werden und sie sollten daher vorl¨aufigals Exoplanet-Kandidaten bezeichnet werden. Misst man das astrometrische Signal eines planetaren oder massearmen Begleiters, indem man die Reflexbewegung des Hauptsterns vermisst, so erh¨altman den vollen Satz an orbitalen Parametern. Mit dieser Information kann die genaue Masse der Kandidaten bestimmt werden und es ist somit m¨oglich, die Planetenkandidaten als wahre Exoplaneten, Braune Zwerge oder massearme Sterne einzustufen. Im Rahmen der vorliegenden Doktorarbeit wurde ein Zwergstern der Spektralklasse M, der einen mittels Radialgeschwindigkeitsmessungen entdeckten wahrscheinlichen Braunen Zwerg als Begleiter hat, innerhalb eines fortlaufenden Beobachtungsprogramms zur Detektion des astrometrischen Signals beobachtet. Bodengebundene Beobachtungen mit dem Adaptiven Optik (AO) Instrument ESO/NACO wurden durchgef¨uhrt,um die wahre Natur des Begleiters zu bestimmen (Brauner Zwerg oder massearmer Stern) und die Aussichten dieser Technik im Bereich der Planetenendeckung zu untersuchen. Die astrometrischen Korrekturen, notwendig um hochpr¨aziseAstrometrie zu betreiben, werden in diesem Zusammenhang beschrieben und ihr Beitrag zur Gesamtmessge- nauigkeit untersucht. Die großen Unsicherheiten in der Messgenauigkeit der Anderung¨ der Pixel-Skala und der Ausrichtung des Detektors verhinderten jedoch, das Signal des astrometrischen Orbits zu messen. Die Abbildungsqualit¨ateines bodengebundenen Teleskopes ist begrenzt durch die Tur- bulenz in der Atmosph¨areder Erde. Die dadurch hervorgerufenenen Verformungen der Lichtwellen k¨onnenmit Hilfe der Technik der Adaptiven Optik vermessen und kor- rigiert werden und somit beinahe beugungsbegrenzte Abbildungen erzeugt werden. Im Fall der klassischen AO mit nur einem Referenzstern ist die Korrektur jedoch nur in einem engen Bereich um den Referenzstern m¨oglich. Multikonjugierte Adaptive Op- tik verwendet mehrere Referenzsterne, um ein gr¨osseresGesichtfeld zu korrigieren. Das MAD Instrument wurde gebaut und am Very Large Telescope installiert, um diese neue Technik zu demonstrieren. Beobachtungen mit MAD wurden im Rahmen dieser Arbeit auf ihre astrometrische Genauigkeit hin ausgewertet. Dabei wurden zwei Datens¨atze verglichen, die in unterschiedlichen Korrektur-Modi aufgenommen wurden: zum einen wurde nur die Turbulenzschicht nahe am Boden korrigiert, zum anderen die volle mul- tikonjugierte Konfiguration des Instrumentes genutzt. ii for my father in loving memory iii iv Contents 1 Introduction 1 1.1 Orbital Elements . 3 1.2 Detection Methods . 4 1.2.1 Pulsar Timing . 4 1.2.2 Radial Velocity Measurements . 4 1.2.3 Transits . 6 1.2.4 Gravitational Microlensing . 8 1.2.5 Direct Imaging . 8 1.2.6 Astrometry . 11 1.3 Brown Dwarfs . 15 1.3.1 Brown Dwarf Formation Processes . 17 1.3.2 The Brown Dwarf Desert . 17 1.4 Goal of this Work . 18 2 Introduction to Adaptive Optics 21 2.1 Atmospheric Turbulence . 23 2.1.1 Fried-Parameter . 25 2.1.2 Time Dependent Effects . 25 2.2 Principles of Adaptive Optics . 25 2.2.1 General Setup of an AO System . 26 2.2.2 Strehl Ratio . 27 2.2.3 Anisoplanatism . 27 2.3 NACO . 28 2.3.1 Our Observation Configuration . 30 v 3 Observations and Data Reduction 31 3.1 The Target Field . 31 3.2 The Reference Field . 33 3.3 Adaptive Optics Observations of GJ 1046 . 35 3.4 Data Reduction . 38 3.4.1 Sky Subtraction . 39 3.4.2 50 Hz Noise . 40 3.4.3 Shift and Add . 40 4 Analysis and Astrometric Corrections 41 4.1 Position Measurements . 41 4.1.1 Positional Error Estimate - Bootstrapping . 43 4.2 Astrometry with FITS-Header Keywords . 43 4.2.1 World Coordinates in FITS . 43 4.2.2 Celestial Coordinates in FITS . 46 4.2.3 Transformation from xy-Coordinates into RA/DEC . 46 4.3 Astrometric Corrections . 47 4.3.1 Theory of Atmospheric Refraction . 47 4.3.2 Differential Atmospheric Refraction . 50 4.3.3 Correction for Differential Refraction . 51 4.3.4 Errors from Differential Refraction Correction . 55 4.3.5 Theory of Aberration . 56 4.3.6 Correction for Differential Aberration . 59 4.3.7 Errors from Differential Aberration Correction . 60 4.3.8 Light Time Delay . 60 4.3.9 Differential Tilt Jitter . 61 4.3.10 Parallax . 62 4.3.11 Proper Motion . 64 4.4 Plate-scale and Detector Rotation Stability . 66 4.4.1 Plate-scale Correction . 69 5 The Orbit Fit 73 vi 5.1 Preparing the Coordinates for the Orbital Fit . 73 5.2 Theory of Deriving the Orbital Elements . 76 5.2.1 The Thiele-Innes Constants . 77 5.3 The Astrometric Orbit Fit . 79 6 Results 83 6.1 The Orbit . 83 6.2 Discussion and Conclusion . 86 7 Introduction to MCAO and MAD 91 7.1 MCAO - The Next Generation of Adaptive Optics . 91 7.1.1 Star Oriented Approach . 92 7.1.2 Layer Oriented Approach . 92 7.1.3 Ground Layer Adaptive Optics . 93 7.1.4 Current and Future MCAO Systems . 93 7.2 MAD - Multi conjugated Adaptive optics Demonstrator . 94 7.3 Goal of this Work . 96 8 Astrometry with MAD 97 8.1 Observations . 97 8.1.1 GLAO - 47 Tuc . 97 8.1.2 MCAO - NGC 6388 . 99 8.2 Data Reduction . 100 8.3 Strehl Maps . 104 8.4 PSF Tests . 107 8.5 Position Measurements . 112 8.6 Ensquared Energy . 114 8.7 Distortion Mapping . 115 9 Results 117 9.1 Separation Measurements . 118 9.2 Residual Mapping . 120 9.3 Mean Positions . 123 vii 9.4 Discussion and Conclusion . 126 A Strehl plots 129 B Acronyms 137 Bibliography 148 viii List of Figures 1.1 Definition of the orbital elements. 3 1.2 Radial velocity curve of the system HD 209458 . 6 1.3 Transit light curves for the planetary system HD 209458 . 7 1.4 Light curve of a gravitational lensing event of a star with a planet . 9 1.5 Image of the three planetary companions to the star HR 8799 . 10 1.6 Examples of astrometric motions of stars due to planets . 13 1.7 Brown dwarf desert in mass and period . 19 2.1 The Point-Spread-Function (PSF) of a point source . 22 2.2 Effect of atmospheric turbulence on the image of a star . 23 2.3 Structure of the atmosphere with typical turbulence profile. (Hardy, 1998) 24 2.4 Principle setup of an AO system. 26 2.5 Angular Anisoplanatism . 28 3.1 RV time series of GJ 1046 . 33 3.2 Time series of the movement of GJ 1046 on the sky . 34 3.3 NACO image of GJ 1046 and the reference field in the globular cluster 47 Tucanae from July 2008. 35 3.4 GJ 1046 observations overplotted over a simulated orbit . 37 3.5 Jitter pattern for the target and reference field . 39 4.1 Stepwise description of the corrections applied to the measures pixel coordinates of the stars. 42 4.2 Conversion of pixel coordinates to world coordinates (after Calabretta and Greisen (2002)). 45 4.3 Refraction in the atmosphere. For more details see text. 48 4.4 Differential refraction . 52 ix 4.5 Sign of the differential refraction correction during different times of observations . 54 4.6 Stellar aberration . ..
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