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Gravitational Lensing An Introduction

Gravitational Lensing An Introduction. Suprit Singh. CRUX. Deflection of Light by Gravitating Bodies. Point Mass Lens. Simplest Situation : This is the lens equation relating real and apparent position of the source. For point-like lens. Point Mass Lens.

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Gravitational Lensing An Introduction

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  1. Gravitational LensingAn Introduction Suprit Singh

  2. CRUX • Deflection of Light by Gravitating Bodies

  3. Point Mass Lens • Simplest Situation : • This is the lens equation relating real and apparent position of the source. • For point-like lens

  4. Point Mass Lens • When Source and lens are aligned : Einstein Ring is formed • Also when Extended lens has spherical symmetry and source lies on the symmetry axis. • For Generic position of the source , there exist two images :

  5. Extended Lens System • We make thin lens approximation : Taking surface mass distribution where z is the light ray direction. • Then for linearized case : • Introducing projected gravitational potential satisfying

  6. Extended Lens System • For Spherically symmetric lens : Employ Divergence theorem where • The lens equation thus is (with rescaled potential)

  7. Lensing Astrophysics • Counting lens systems gives a mass-biased census of the universe not the usual luminosity-biased one. The best way of locating compact dark objects. • The number of lenses depends on the cosmological geometry (particularly the cosmological constant) • Time delays give us a distance measuring technique; i.e. the Hubble constant (H0).

  8. Lensing by galaxies • At cosmological distances galaxies deflect radiation by about an arcsecond • The mass is distributed => the deflection depends on impact parameter and reflects the mass distribution. • About 1 in 600 quasars are sufficiently lined up with an intervening galaxy to be lensed. • Some galaxies contain dust and therefore may hide the images they produce in the optical. • One reason why radio searches are best

  9. Image configurations • There is a range of image configurations. Depends on the complexity of the mass distribution and impact parameter. • 2-image (doubles) • 4-image (quads) • 6-image • Einstein rings

  10. Images • Circular symmetry => doubles • Elliptical mass distributions => doubles or quads. Depends on impact parameter • Perfect alignment gives Einstein ring (or Einstein cross) • More complex mass distributions => higher multiplicities. (6-image system known)

  11. CLASS Lens Systems (Cosmic Lens All-Sky Survey) 1600+434 1608+434 2045+265

  12. Thank You

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