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14.20 o1 m miller
14.20 o1 m miller
14.20 o1 m miller
14.20 o1 m miller
14.20 o1 m miller
14.20 o1 m miller
14.20 o1 m miller
14.20 o1 m miller
14.20 o1 m miller
14.20 o1 m miller
14.20 o1 m miller
14.20 o1 m miller
14.20 o1 m miller
14.20 o1 m miller
14.20 o1 m miller
14.20 o1 m miller
14.20 o1 m miller
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14.20 o1 m miller

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Research 1: M Miller

Research 1: M Miller

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  • 1. Discovering Extrasolar Planets via Gravitational Microlensing Michael Miller Denis Sullivan
  • 2. Overview Introduction to Gravitational Microlensing Multiple lens systems  Complex representation Analysing data Concluding remarks
  • 3. What is Gravitational Microlensing? Bending of light in a weak gravitational field  Gravitational field from a star or planet The path of the light bends by a small angle as it passes the star or planet Observer “sees” image of star slightly shifted from source Image Source b M Observer Lens
  • 4. Gravitational Microlensing– Single Lens  Two approximations:  Thin lens approximation  Small angle approximation  φ ≈ sin(φ) ≈ tan(φ) θE Observer DSSource plane DSL Lens plane DL
  • 5. Gravitational Microlensing– Single Lens Lens Equation θ+ β θE θ- Observer DSSource plane DSL Lens plane DL
  • 6. Gravitational Microlensing– Single Lens Lens Equation
  • 7. Gravitational Microlensing– Single Lens Lens Equation θ+ z+ β w θ z-- θE 1
  • 8. Gravitational Microlensing– Single Lens  Intrinsic brightness of the source, does not change  Intensity per unit area in each image is the same as the source  Magnification, M, is the ratio of observed light, to amount of light if there was no lensing
  • 9. Multiple Lenses– Two Lenses Star + planet (or binary stars) Lens Equation y z r2 w z r1 z x Observer Source plane Lens plane  Positions represented by vectors
  • 10. Multiple Lenses– Two Lenses Star + planet (or binary stars) Lens Equation y Cannot be solved analytically Solved numerically z  Inverse-Ray Tracing r2 w z  “Brute force approach” r1 z x  Semi-Analytical Method  Positions represented by vectors
  • 11. Multiple Lenses– Two Lenses Star + planet (or binary stars) Lens Equation Five roots  Five images? iy 3 or 5 images Numerically solve polynomial z r2 using Jenkins-Traub algorithm z w Substitute z back into Lens r1 z x Equation  recalculated w = source position w  z is physical image  recalculated w ≠ source position w  Positions represented by complex numbe  z is not physical image
  • 12. Multiple Lenses Star + planets Lens Equation For N lenses y No. of roots = N2 + 1 z Numerically solve polynomial z r4 r2 using Jenkins-Traub algorithm w z Substitute z back into Lens r1 x Equation r3  recalculated w = source position w z z  z is physical image  recalculated w ≠ source position w  Positions represented by complex numbe  z is not physical image
  • 13. Multiple Lenses- Three Lenses 3 lens animation
  • 14. Analysing Data Separation between images is ~milliarcseconds  Cannot be resolved! Magnification can be measured! Microlensing events recorded by measuring apparent brightness over time (light curve) Fit together data from different collaborations MOA OGLE  Fit theoretical light curve to data microFUN
  • 15. Analysing Data Light curve parameters  Mass ratio(s)  Einstein crossing time  Source radius Depend on Mass  Impact parameter OGLE In units of θE MOA  Lens position(s)  Lens separation(s) + angle(s)  Lens Motion  Parallax χ2: minimised! microFUN Least squares fit  Vary parameters to minimise χ2  When χ2 is minimised, values for parameters are parameter values for event
  • 16. Concluding remarks Exact values for θE and total mass cannot be determined directly from microlensing light curve Advantages:  Not dependent on light from host star  Free-floating planets  Not limited by distance from Earth  Gives snap-shot of planetary system in short observing time Disadvantage:  Alignments of two stars are rare  Follow-up (repeated) measurements difficult
  • 17. Acknowledgements VUW Optical Astrophysics Research Group Marsden Fund MOA Collaboration  (Microlensing Observations in Astrophysics)

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