Gravitational lensing

Gravitational lensing - Gravitational lensing at last here...

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Gravitational lensing: at last, here is a probe which is unbiased by the luminosity of a target as long as it's transparent. Dark matter is quite transparent; that's the problem. This phenomenon falls out of the principle of equivalence, with a magnitude twice what you would get in a pseudo- Newtonian case assigning the photon a mass hν/c 2 (Einstein 1935 , in Science). Zwicky (1937 Phys. Rev. 51, 290 and 679) first suggested that lensing (in some languages more accurately called the gravitational mirage) would be observable on the scale of galaxies, rather than for stars as originally treated by Einstein. The basic equation gives the angular deflection α as a function of impact parameter of the asymptotic line of sight b (note that one has to be very careful about linear measures when geodisics bend) as as a vector quantity traversing potential Φ ; for spherically symmetric masses (actually cylindrically symmetric is more nearly appropriate) this becomes a scalar deflection and for a point mass α = 4GM/c 2 ; for a spherically symmetric mass distribution, this is generalized by letting M be the enclosed mass (within the deflected beam) M(b) (not the same as M(r) ), following, for example, Refsdal 1964 (MNRAS 128, 295) and Young et al. 1980 (ApJ 241, 507). The obvious integration holds for extended masses, with the approximation frequently possible that b is small compared to the line-of-sight distance. For a more galaxy-like potential
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This note was uploaded on 11/10/2011 for the course AST AST1002 taught by Professor Emilyhoward during the Fall '10 term at Broward College.

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Gravitational lensing - Gravitational lensing at last here...

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