A Short Talk on…

Gravitational Lensing

Presented by: Anthony L, James J, and Vince V.

What is Gravitational lensing?

● A process where light is bent due to gravity of a massive body.

● Results in multiple images of the source created.

● Massive bodies such as galaxy clusters and blackholes serves as a gravitational lens.

Origin of Gravitational Lensing

● First predicted by Albert Einstein in 1905 when he was working on his theory of General Relativity.

• Einstein’s predictions were confirmed by Sir Arthur Eddington in 1919 through his observations of the solar eclipse in Principe, Africa.

Eddington’s Experiment

The Deflection Angle

● One notion to keep in mind is that we will be deriving the deflection angle in the Schwarzschild exterior vacuum space-time.

● In the Schwarzschild space-time the deflection angle is given by the expression

● This is just twice the expression that Newton’s theory of gravity predicts, provided that

● For a three-dimensional mass distribution with a volume density , the deflection angle becomes

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The Lens Equation

● Since , . Thus by imposing the small angle approximation we can find an expression for the true position of a source as

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The Lens Equation Con’t

● The scaled deflection angle in terms of the mass density is

● where with● For the case where , the mass distribution

will produce several images. Thus is the dividing line between ‘weak’ and ‘strong’ gravitational lenses.

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Strong Gravitational Lensing

● Strong gravitational lensing is an effect that is strong enough to produce multiple images, arcs, or even Einstein rings.

● Almost always, there are an odd number of images formed.

Weak Gravitational lensing● In most cases the lens is

not strong enough to form multiple images or arcs.

● The background galaxies, however, are still distorted

● They are stretched and magnified, but by such small amounts that it is difficult to measure.

Gravitational Microlensing● Microlensing occurs when a massive foreground object passes between the

observer and the source being observed.

● The Einstein angle is angular radius of the Einstein ring in the event of perfect alignment given by

● During a microlensing event, the brightness of the source is amplified by an amplification factor A, given by

● In practice, source size effects set a limit to how large an amplification can occur for a very close alignment.

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Applications of Gravitational Lensing

Expanding the range of our observations

Data on older and more distant galaxy populations provides tests for models of galactic evolution

“Weighing” galaxies and galaxy clusters, mapping mass distribution (including dark matter)

Measuring constants such as H0

Searching for dark matter in the Milky Way (particularly in the halo, and towards the galactic bulge)

Planet hunting

Determining the degree by which light from the source is deflected allows calculation of the lens mass

The shape and distribution of the images produced by the lensing effect reveal the distribution of mass within the lensing object

Strong and Weak Lensing

Different images of the same source object represent light which has taken different paths from the source to us; different paths means different transit time

Time delay between various images is proportional to Hubble's constant, the shape of the lens, and the relative distances between us, the lens and the source

Thus Hubble's constant can be estimated based on the lensing effect

Mapping dark matter

Large-scale maps of dark matter distribution can be derived from analysis of weak lensing effects over large areas of sky

<== Map derived from COSMOS survey

Also useful on smaller scales, for studying individual galaxy clusters

Bullet Cluster

Optical image from HST

Chandra X-ray image showing distribution of hot intergalactic gas (probably most of the cluster's baryonic mass)

Tomographic map of overall mass distribution, based on weak lensing studies

Microlensing

Surveys of microlensing events within the Milky Way search for dark matter in the form of Massively Compact Halo Objects

MACHOs are “normal” baryonic matter such as brown dwarfs

Based on surveys to date, only a small percentage (<20%) of halo dark matter can be attributed to MACHOs

Surveys also conducted towards the galactic

bulge – one remarkable image at left is a

reconstructed image of MOA 2002-BLG-33,

a highly microlensed source star, accurate to

within 4 x 10-8 arcsec

Stellar atmospheres?

Planet hunting

Planets in orbit around microlensing stars cause telltale distortions in the source star's light curve

OGLE 2005-BLG-390Lb