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Astrophysical applications of gravitational microlensing By Shude Mao Ziang Yan Department of Physics,Tsinghua

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Introduction: Gravitational Lensing According to GR, when a ray of light passes by a massive object, the gravitational field will deflect the ray just like light refraction. When the source is very close to the line between the observer and the massive object, the “gravitational refraction” make the massive object act like a “lens”. Fig.1

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Introduction: Phenomenon of GL Fig.2 Cover of Gravitational Lensing:Strong, Weak and Micro

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Introduction: Phenomenon of GL Fig.3 Einstein Ring (a lensing of a galaxy)

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Introduction: Phenomenon of GL Fig.4 lensing by several galaxies

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Introduction:Category of GL Microlensing by stars(GM) Multiple-images by galaxies Giant arcs and large-separation lenses by clusters of galaxies

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Basics of GM: Image Positions Some approximation: 1.The source(S), lens(D) and the observer(O) is nearly on a straight line. 2.Neglect the size and structure of the lens and the source. Fig.5

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Basics of GM: Image Positions Fig.5

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Basics of GM: Image Positions Fig.5

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Basics of GM: Image Positions Fig.6 Separated images

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Basics of GM: Magnifications Fig.7

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Basics of GM:Light Curve Fig.8

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Basics of GM: Light Curve Fig.8 Light curve of a lensing event

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Basics of GM: Degeneracy and Non-standard models

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Basics of GM:N-point Lens GM

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Basics of GM: Critical Curves and Caustic When J=0 in (16), the magnification will turn to infinity(in fact because of the finite size of the source and lens the magnification just have a sharp peak). The image position satisfying J=0 forms critical curves, which are mapped into caustics in the source plane.

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Basics of GM: Critical Curves and Caustic Fig.9 Critical curves and caustic in a binary system

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Basics of GM: Optical Depth and Event Rates

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Applications of GM 1.Detect the main composition in the galactic halo. From the detections of MACHOs by microlensing, it is concluded that only ≤2%of the halo could be MACHOs. While earlier research 20%. 2.Detect the galactic structure. With analyzing the optical depth and event rate. 3.Analyze the stellar atmosphere and bulge formation Microlensing can magnify the signal-to-noise ratio. 4.Detect exoplanets

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Applications of GM: Detect Exoplanets Fig.10 A super-Earth (≈ 5.5M ⊕ ) discovered by microlensing.

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Applications of GM: Detecting Exoplanets Fig.11 The first two-planet system discovered by Gaudi et al.

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Applications of GM: Detecting Exoplanets Fig.12 Extrasolar planets in the plane of mass vs. separation (in units of the snow line, indicated by the vertical dashed green line). The red filled circles with error bars indicate planets found by microlensing. The black triangles and blue squares indicate the planets discovered by radial velocities and transits, respectively. The magenta and green triangles indicate the planets detected via direct imaging and timing, respectively.

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Future of GM There are still much problems unsolved in the calculation of GM. e.g. The degenerate in the parallax events; how to distinguish exoplanet system with binary system; the number of critical curves and image numbers in a topological sense. There are more and more collaborations participate in the detection of GM like OGLE, MOA, SKYMAPPER and so on. Chinese scientists also make their distributions.

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