Extrasolar Moons as Gravitational Microlenses Christine Liebig

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Chapter 4 Choice of Scenarios This chapter presents the assumptions that we used for our simulations. We open with a detailed discussion of the astrophysical parameter space that is available for simulations of a microlensing system consisting of star, planet and moon. We separate the parameters into those that are relevant for the creation of magnification patterns (section 4.1), and those necessary for the physical interpretation of the microlensing light curves (section 4.2). By choosing the most probable or in some other way most reasonable value for each of the parameters (the reasons for our choices are explained within the first two sections of this chapter), we create a standard scenario (section 4.3) that all other parameters are weighted against during the analysis. host star qP S = MPlanet MStar dP S qMP = MMoon MPlanet φ planet moon Figure 4.1: For creating the magnification maps, five parameters have to be fixed. They are the relative masses qP S and qMP as well as the angular separations in the lens plane dP S and dMP and the position angle of the moon φ. These parameters determine the relative projected positions of the three bodies. 4.1 Parameters Relevant for Magnification Patterns There are five parameters describing the lens configuration (see figure 4.1). They are the mass ratios qP S = MPlanet MStar and qMP = MMoon , then the angular separations MPlanet 31 dMP
32 4.1. PARAMETERS RELEVANT FOR MAGNIFICATION PATTERNS dP S, between planet and star, and dMP , between moon and planet, and as the fifth parameter φ, the position angle of the moon with respect to the planet-star axis. These five parameters are barely constrained by the physics of a three-body system, even if we do require mass ratios very different from unity and separations that allow for stable orbits. Therefore it is quite impossible for us to cover the whole zoo of possible magnification patterns. 4.1.1 Mass ratio of planet and star The mass ratio of planet and star qP S = MPlanet is chosen to match realistic settings. MStar Since we have declared an interest in planets (and not binary stars), we choose a small value of qP S. Our standard value will be 10−3 which is the mass ratio of Jupiter and the Sun, or could be a Saturn-mass planet around an M-Dwarf of 0.3 M⊙. Please refer also to the discussion of the stellar mass, section 4.2.3. At a given projected separation between star and planet, this mass ratio determines the size of the planetary caustic, with a larger qP S leading to a larger caustic. This is illustrated in figure 4.2. We will also vary qP S to examine scenarios with mass ratios corresponding to a Jovian mass around an M-dwarf and to a Saturn mass around the Sun, respectively. (a) qP S = 3.3 × 10 −3 (b) qP S = 10 −3 (c) qP S = 3.0 × 10 −4 Figure 4.2: The size of the planetary caustic depends on the mass ratio qP S of planet and star. Shown are wide-angle magnification patterns, with a side length of 1.6 θE, that include the central caustic of the star as well as the planetary caustic. From left to right the value of the planetary mass ratio decreases, and the size of the planetary caustic decreases accordingly. All other parameters are frozen. 4.1.2 Mass ratio of moon and planet To be classified as a moon, the tertiary body must have a mass considerably smaller than the secondary. The standard case in our examination corresponds to the Moon/Earth mass ratio of qMP = MLuna MEarth = 10−2 . We are generous towards the higher mass end, and include a mass ratio of 10 −1 in our analysis, corresponding to the Charon/Pluto system, i.e. a double planet (or double plutoid, if you want).
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Page 11 and 12: 2 CONTENTS 5 Results: Detectability
Page 13 and 14: 4 first confirmed detection by the
Page 15 and 16: 6 Figure 1.1: The solar system seen
Page 17 and 18: 8 2.2. BASIC EQUATIONS and publish
Page 19 and 20: 10 2.2. BASIC EQUATIONS We can inte
Page 21 and 22: 12 2.2. BASIC EQUATIONS −∆mag F
Page 23 and 24: 14 2.3. SEARCH FOR PLANETS VIA GALA
Page 25 and 26: 16 3.1. MAGNIFICATION PATTERNS 3.1
Page 27 and 28: 18 3.2. LIGHT CURVES Figure 3.1: A
Page 29 and 30: 20 3.2. LIGHT CURVES 3.2.2 Light cu
Page 31 and 32: 22 3.3. STATISTICAL ANALYSIS origin
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Page 35 and 36: 26 3.3. STATISTICAL ANALYSIS detail
Page 37 and 38: 28 3.3. STATISTICAL ANALYSIS We use
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Page 45 and 46: 36 4.1. PARAMETERS RELEVANT FOR MAG
Page 47 and 48: 38 4.2. PARAMETERS RELEVANT FOR LIG
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Page 54 and 55: Chapter 5 Results: Detectability of
Page 56 and 57: CHAPTER 5. DETECTABILITY OF EXTRASO
Page 62 and 63: Chapter 6 Conclusion We showed that
Page 64 and 65: Appendix A Analysed Magnification P
Page 66 and 67: APPENDIX A. ANALYSED MAGNIFICATION
Page 74 and 75: Appendix B Numerical Results In thi
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Page 79 and 80: 70 BIBLIOGRAPHY Bevington, Philip R
Page 81 and 82: 72 BIBLIOGRAPHY eprint arXiv:0803.4
Page 83 and 84: 74 BIBLIOGRAPHY Sartoretti, Paola a
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Page 87 and 88: 78 BIBLIOGRAPHY Gabriele Maier. I t

Extrasolar Moons as Gravitational Microlenses Christine Liebig

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