Galactic aspects of gravitational microlensing: high magnification events and stellar limb darkening of a source star in the galactic bulge [Elektronische Ressource] / presented by Marta Zub

Dissertationsubmitted to theCombined Faculties for the Natural Sciences and for Mathematicsof the Ruperto-Carola University of Heidelberg, Germanyfor the degree ofDoctor of Natural Sciencespresented byDiplom-Physikerin Marta ZubBorn in Zielona Go´ra, PolandOral examination: 6 Mai 2009Galactic Aspects of GravitationalMicrolensing:High Magnification Events and Stellar Limb-darkening of a SourceStar in the Galactic bulgeReferees: Prof. Dr. Joachim WambsganßProf. Dr. Andreas QuirrenbachZusammenfassungDer Mikro-Gravitationslinseneffekt ist ein wertvolles Werkzeug um extrasolare Planeten umSterne im Abstand von wenigen kpc zu finden. Die Vermutung eines Planetensignals in denzwei hochversta¨rkten Mikrolinsenereignissen OGLE 2006-BLG-245 und MOA 2006-BLG-099veranlasste uns, eine detaillierte Modellierung und Analyse vorzunehmen. Basierend auf demVergleich modellierter Einzel- und Doppellinsensysteme zeigten wir, dass die Abweichungenin den beobachteten Lichtkurven nicht durch einen planetaren Begleiter verursacht wurden.Unsere Modellierung und Analyse vier weiterer hochversta¨rkter Mikrolinsenereignisse veran-schaulicht die Mo¨glichkeit, die Detektionseffizienz von Mikrolinsen-Datensa¨tzen hinsichtlichplanetarer Begleiter zu untersuchen. Wir analysieren ausserdem das Einzellinsenereignis OGLE -2004-BLG-482, welches dazu benutzt wurde das Helligkeitsprofil des gelinsten Hintergrund-sterns im galaktischen Bulge zu messen.
Publié le : jeudi 1 janvier 2009
Lecture(s) : 24
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Source : ARCHIV.UB.UNI-HEIDELBERG.DE/VOLLTEXTSERVER/VOLLTEXTE/2009/9479/PDF/PHD_THESIS_MARTAZUB.PDF
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Dissertation
submitted to the Combined Faculties for the Natural Sciences and for Mathematics of the Ruperto-Carola University of Heidelberg, Germany for the degree of Doctor of Natural Sciences
presented by
Diplom-Physikerin Marta Zub BorninZielonaG´ora,Poland
Oral examination: 6 Mai 2009
Galactic Aspects of Gravitational Microlensing: High Magnication Events and Stellar Limb-darkening of a Source Star in the Galactic bulge
Referees: Prof. Dr. Joachim Wambsganß Prof. Dr. Andreas Quirrenbach
Zusammenfassung Der Mikro-Gravitationslinseneffekt ist ein wertvolles Werkzeug um extrasolare Planeten um Sterne im Abstand von wenigen kpc zu nden. Die Vermutung eines Planetensignals in den zweihochverst¨arktenMikrolinsenereignissenOGLE2006-BLG-245undMOA2006-BLG-099 veranlasste uns, eine detaillierte Modellierung und Analyse vorzunehmen. Basierend auf dem Vergleich modellierter Einzel- und Doppellinsensysteme zeigten wir, dass die Abweichungen in den beobachteten Lichtkurven nicht durch einen planetaren Begleiter verursacht wurden. UnsereModellierungundAnalysevierweitererhochverst¨arkterMikrolinsenereignisseveran-schaulicht die Mo¨glichkeit, die Detektionsefzienz von Mikrolinsen-Datensa¨tzen hinsichtlich planetarer Begleiter zu untersuchen. Wir analysieren ausserdem das Einzellinsenereignis OGLE -2004-BLG-482, welches dazu benutzt wurde das Helligkeitsprol des gelinsten Hintergrund-sterns im galaktischen Bulge zu messen. Wir fu¨hrten die Datenreduktion und Analyse hochaufge-lo¨ster Lichtkurven dieses Ereignisses durch, welche von den Kollaborationen PLANET, OGLE und MicroFUN mitI,Rund Klar-Filtern aufgenommen wurden. benutzten ein hochauf- Wir gel¨ostesVLT/UVES-Spektrum,nahederMaximalverst¨arkungaufgenommen,umfundamen-taleParameterdesQuellsternszubestimmen,welchersichalsk¨uhlerM3-Riesensternmit Teff=3667±150 K, logg=21±10 entpuppte. detaillierte Mikrolinsen-Modellierung Die der Lichtkurve erlaubte uns Randverdunkelungskoefzienten zu bestimmen und stellt damit eine Diagnose solcher Messungen durch den Mikrolinseneffekt bereit. Der Vergleich unserer Ergebnisse mit Vorhersagen von Modellatmospha¨ren fu¨r die entsprechenden stellaren Parame-ter zeigt, dass diese sehr gut sowohl mit den linearen Randverdunkelungsgesetzen als auch mit alternativen Randverdunkelungsprolen, gewonnen aus einer Hauptkomponentenanalyse von ATLAS-ModellenvonSternenatmospha¨ren,¨ubereinstimmen.
Abstract Gravitational microlensing provides a powerful tool to search for extrasolar planets of stars at distances of order of several kpc. The suspicion of a planetary signal in the two high magnica-tion events OGLE 2006-BLG-245 and MOA 2006-BLG-099 led us to perform a detailed mod-elling and analysis of those two events. Based on the comparison of single-lens and binary-lens models, we demonstrate that the observed light curve deviations are not caused by a planetary companion. Our modelling and analysis of four other high magnication events illustrate the possibility to study detection efciencies of microlensing data sets to planetary companions. We also present a detailed study of the single-lens OGLE 2004-BLG-482 microlensing event, used to measure the brightness prole of the background lensed star located in the Galactic bulge. We performed data reduction and analysis of well sampled observations of this event obtained by the PLANET, OGLE and MicroFUN collaborations in theI,Rand clear lters. We also used a high resolution spectrum obtained with VLT/UVES close to the peak of the light curve to determine the fundamental parameters of the source star, that we nd to be a cool red M3 giant withTeff=3667± log150 K,g=21±10. We then performed a detailed microlensing modelling of the light curve to measure linear limb-darkening coefcients and to provide new diagnostics of such measurements through microlensing. We compare our results to model-atmosphere predictions based on limb-darkening coefcients for the corresponding stellar parameters. Our limb-darkening measurements agree very well with predictions of the model atmosphere, for both linear limb-darkening laws and alternative limb-darkening proles based on a principal component analysis of ATLAS stellar atmosphere models.
Contents
1 Introduction 2 A Review of Gravitational Lensing 2.1 Gravitational lensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 The lens equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 The gravitational microlensing effect . . . . . . . . . . . . . . . . . . . . . . . 2.4 Source ux magnication. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Microlensing light curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Binary lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Critical curves and caustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 A nite source effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8.1 Limb darkening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Microlensing Data Collection, Analysis and Photometry 3.1 OGLE and MOA Microlensing Surveys . . . . . . . . . . . . . . . . . . . . . 3.2 Microlensing Follow-up Networks: PLANET and MicroFUN . . . . . . . . . . 3.3 Photometry and Analysis Techniques . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Method of Photometry . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Data Fitting and Minimisation Methods . . . . . . . . . . . . . . . . . 3.4 Red Clump Giants Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Planet Detection through Microlensing 4.1 Planetary Microlensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 High Magnication Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Analysis of 2006 High Magnication Events. . . . . . . . . . . . . . . . . . . 4.3.1 Selection of 2006 High Magnication Events . . . . . . . . . . . . . . 4.3.2 PSPL models of 2006 High Magnication Events . . . . . . . . . . . . 4.4 Modelling of OGLE 2006-BLG-245 . . . . . . . . . . . . . . . . . . . . . . . 4.5 MOA 2006-BLG-099 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Conclusion on the 2006 High Magnication Events . . . . . . . . . . . . . . . 5 A Detailed Study of Extended Source Event: OGLE 2004-BLG-482 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Photometry – Data Reduction and Analysis . . . . . . . . . . . . . . . . . . . 5.3 Linear limb-darkening formalism . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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CONTENTS
5.4.1 Single-lens, extended-source models . . . . . . . . . . . . . . . . . . . 5.4.2 Fitting data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.3 Estimates of the lens properties . . . . . . . . . . . . . . . . . . . . . 5.5 Calibrated colour-magnitude diagram . . . . . . . . . . . . . . . . . . . . . . 5.6 Source star properties from the photometry and spectroscopy . . . . . . . . . . 5.6.1 Conclusion on the source MK type and parameters . . . . . . . . . . . 5.7 Discussion of the linear limb-darkening coefcients . . . . . . . . . . . . . . . 5.8 Principal Components Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Conclusions and Prospects
Publications
List of gures
Bibliography
Acknowledgements
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Chapter 1
Introduction
In 1915, the theory of General Relativity by Einstein brought for the rst time the proof that a massive body could inuence the path of light rays. Some of the most popular manifestation of light deection are the images of distant galaxies which are distorted into giant luminous arcs.Gravitationallensing”hassincebecomeaveryfruiftulbranchofastrophysics,revealing the presence of dark objectsviatheir mass, or magnifying the ux of objects at cosmological distances, such as quasars (e.g. Walsh et al. 1979,for the rst observed lensed quasar, Q 0957+ 561A,B). In 1936, Einstein considered a conguration where two starsin the Milky Way are almost exactly aligned with an observer, and found that the background star would be seen as a bright ring (the “Einstein ring”). However, he concluded that the nowadays so-called “microlensing effect” would never be detectable, because the angular dimension of the Einstein ring is much too small(around half of a milliarcsec). But fty years later, in 1986, Paczyn´ski published a fundamental article where he proposed a strategy which allow the detection of microlensing eventstowardtheMagellanicClouds.Shortlyafter,Mao&Paczy´nski(1991)demonstrated that observing in the direction of the Galactic bulge would also lead to detectable microlensing events. Although a challenging experiment, two main collaborations formed to check these ideas, EROS and MACHO, and succeeded in 1993 in observing the rst ever microlensing events (Alcock et al. 1993; Aubourg et al. 1993). AnotherimportantconclusionofMao&Paczy´nski(1991)wasthatbyprobingthewhole dark content of the Galactic disc, the microlensing technique was also able to detect very small objects, such as extrasolar planets. Once again, predictions were conrmed, and in 2003, the rst planet detected by microlensing (MOA 2003-BLG-53OGLE 2003-BLG-235, Bond et al. 2004) provided the evidence of the strength of gravitational lensing. In 2005, microlensing was pioneer in unveiling a new class of planets, the now on so-called “Super-Earths”, by the discov-ery of OGLE 2005-BLG-390Lb, a rocky and icy55Mplanet. These rocky planets of mass around 220M 2008, microlensing Inare currently major targets of planet search projects. has conrmed its potency to discover very low-mass planets with the detection of MOA-2007-BLG-192Lb (Bennett et al. 2008), a33M. All the planets discovered by microlensing are located at several kpc, where no other method is able to probe the planet population. Galactic gravitational microlensing is also one of a few techniques, together with interfer-ometry, transiting extrasolar planets and eclipsing binaries to measure brightness proles. This aspect in stellar astrophysics is very original in the sense it allows to probe the atmosphere of
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stars located in the Galactic bulge, in particular red giants.
1.Introduction
In this thesis, we have studied two aspects of Galactic gravitational microlensing: high magni-cation events to detect the presence of extrasolar planets, and measuring the limb-darkening prole of Bulge stars by using the microlensing effect as a tool.
To understand better the lensing phenomenon, we rst introduce in Chapter 2 the important concepts which will enter in the discussion throughout the thesis. The data reduction process using the difference imaging technique is presented in Chapter 3. The PLANET collaboration of which I am a member and its world-wide network of telescopes are also described. In Chapter 4, we introduce binary and planetary microlensing, and discuss in more detail the case of high magnication events to search for extrasolar planets. The core of the chapter is dedicated to the analysis of six promising high magnication events from theobservational season 2006, includ-ing two interesting candidates which were suspected to hide a planetary signal. In Chapter 5, we perform a detailed analysis of the microlensing event OGLE 2004-BLG-482, to derive precise limb-darkening measurements of the background giant bulge star, that we have compared to stellar atmosphere models. Such microlensing are relatively rare, but contain unique informa-tion of stellar atmospheres and opportunity to test atmosphere models. We nally summarise and conclude in Chapter 6, and underline some of the most promising goals that microlensing can achieve in the future, and how.
Chapter 2
A Review of Gravitational Lensing
We hope this chapter acquaints with a few important questions of gravitational lensing phe-nomenon and presents a briey review of them.
2.1 Gravitational lensing A light ray that passes a massive object, undergoes the deection due to the gravitational po-tential of that mass. The most simple case of lens is a point with massMwhich gravity at a distanceris described by the Newtonian potential 8=GM GM(2. =ru2+z21) Assuming the spherically symmetry of a lens object, for the impact parameteruof light ray much larger than the Schwarzschild radius of lens mass, the deection anglea Thus˜ is small. thea˜ can be approximated by integration along unperturbed ray z (see Fig. 2.1) which yields a˜(u) =4cGM2(u)1u(2.2) whereGis the gravitational constant,M(u)is the deecting mass enclosed within radiusuand uthe impact parameter which indicates the minimum approach distance to the object ofis M mass andcis the speed of light. Most of light deection is assumed to occur within the distancezwhich is much smaller than these ones between an observer and lens and between a lens and source. Thus the lens can be considered a thin sheet and in the plane of it the lens mass distribution is projected (the thin-lens approximation). The mass of lens sheet is characterised by its surface mass densityS S(~u) =ZΛ(~uz)dz(2.3)
2.2 The lens equation To imagine how the gravitational lensing phenomenon happens, the geometric description of it with a single lens illustrated in Fig. 2.2 can be helpful. From this sketch using the Euclidean
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