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New Windows on the Universe

New Windows on the Universe. Jan Kuijpers Part 1: Gravitation & relativity J.A. Peacock, Cosmological Physics, Chs. 1 & 2 Part 2: Classical Cosmology Peacock, Chs 3 & 4. Part 2: Classical cosmology. The isotropic universe (3) Gravitational lensing (4). The isotropic universe.

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New Windows on the Universe

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  1. New Windows on the Universe Jan Kuijpers • Part 1: Gravitation & relativity J.A. Peacock, Cosmological Physics, Chs. 1 & 2 • Part 2: Classical Cosmology Peacock, Chs 3 & 4 New Windows on the Universe

  2. Part 2: Classical cosmology • The isotropic universe (3) • Gravitational lensing (4) New Windows on the Universe

  3. The isotropic universe • The RW metric (3.1) • Dynamics of the expansion (3.2-3.3) • Observations (3.4) New Windows on the Universe

  4. Gravitational lensing • Lense equation; lensing potential (4.1) • Simple lenses (4.2) • Fermat’s principle (4.3) • Observations (4.4-4.6) New Windows on the Universe

  5. The isotropic universe The RW metric (3.1) Define fundamental observers: at rest in local matter distribution Global time coordinate t can be defined as proper time measured by these observers Choose radial coordinate so that either f=1 or g=r2 New Windows on the Universe

  6. The RW metric (3.1) Different definition of comoving distance r: Or dimensionless scale factor: Or isotropic form: New Windows on the Universe

  7. The RW metric (3.1) Or define conformal time: New Windows on the Universe

  8. Redshift Proper (small) separation of two fundamental observers: Hubble’s law Comoving distance between two fo’s is constant: New Windows on the Universe

  9. Dynamics of the expansion (3.2-3.3) GR required: - Birkhoff’s theorem - Integration constant Friedmann eqns: Use RW metric in field eqns (problem 3.1): Newton.: 1. Energy eqn. Take time derivative + energy conservation New Windows on the Universe

  10. Flatness problem • Matter radiation equality: • Recombination: 1+zrec=1000 • Matter dominated and flat: • Radiation dominated and flat: • Vacuum energy (p=-c2 follows from energy conservation): New Windows on the Universe

  11. Observations (3.4) • Luminosity distance: the apparent distance assuming • inverse square law for light intensity reduction • Luminosity L : power output/4 • Radiation flux density S: energy received per unit area per sec Redshift for photon energy and one for rate Angular-diameter distance: the apparent distance based on observed diameter assuming euclidean universe New Windows on the Universe

  12. Gravitational lensing Lensing equation; lensing potential (4.1) Relativistic particles in weak fields (eq. 2.24): Bend angle (use angular diameter distances): Approximation: geometrically thin lenses New Windows on the Universe

  13. Gravitational lenses are flawed!!! New Windows on the Universe

  14. Gravitational imaging New Windows on the Universe

  15. Lensing equation DLS DL DS Flux density from image is: New Windows on the Universe

  16. Lensing potential Notation: - potential! New Windows on the Universe

  17. Simple lenses (4.2) Multiple images DLS Circularly symmetric surface mass density: DL New Windows on the Universe

  18. Einstein ring r S O L New Windows on the Universe

  19. Typical numbers Einstein Radius point mass: ER isothermal sphere: Critical surface density: New Windows on the Universe

  20. Time delays b DLS DL DS • Time lags between multiple images because of: • Path length difference: • 2. Reduced coordinate speed of light (static weak fields): New Windows on the Universe

  21. Fermat’s principle (4.3) Images form along paths where the time delay is stationary Note: differentiation wrt I recovers lens equation. Example: from a to d: introduction of increasing mass (increasing -) leads to extra Stationary points (minima, Maxima, saddle points in ) New Windows on the Universe

  22. Caustics and catastrophe theory New Windows on the Universe

  23. Lens model for flattened galaxy at two different relative distances. a: density contours c: caustics in image plane b: time surface contours d: dual caustics in source plane New Windows on the Universe

  24. Observations (4.4-4.6) Light deflection around the Sun The Sun1.75” New Windows on the Universe

  25. Newton/Soldner versus Einstein New Windows on the Universe

  26. New Windows on the Universe

  27. Total eclipse 21 september 1922 Western Australia, 92 stars (dots are reference positions, lines displacements, enlarged!) New Windows on the Universe

  28. Strong lensing New Windows on the Universe

  29. New Windows on the Universe

  30. Modelling New Windows on the Universe

  31. New Windows on the Universe

  32. New Windows on the Universe

  33. New Windows on the Universe

  34. New Windows on the Universe

  35. Robert J. Nemiroff 1993: Sky as seen past a compact star, 1/3 bigger than its Schwarzschild radius, and at a distance of 10 Schwarzschild radii. The star has a terrestrial surface topography New Windows on the Universe

  36. Sirius Orion Orion Sirius New Windows on the Universe

  37. New Windows on the Universe

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