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A Short Talk on…
Gravitational Lensing
Presented by: Anthony L, James J, and Vince V.
What is Gravitational lensing?
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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
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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
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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
4GM
 2
c
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This is just twice the expression that Newton’s theory of gravity predicts,
RS
provided that 
For a three-dimensional mass distribution with a volume density   r  , the
deflection angle becomes
4G 2
  '
  2  d  '  '
2
c
  '
 
The Lens Equation
●
Since  RS ,  1 . Thus
by imposing the small
angle approximation we
can find an expression
for the true position of a
source as



Dds
  
 Dd      
Ds
The Lens Equation Con’t
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The scaled deflection angle in terms of the
mass density is

  
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●
where   ' 

1

 Dd 
cr

 d  '  '
2
2
with
  '
  '
2
Ds
c2
cr 
4 G Dd Dds
For the case where   cr , the mass distribution
will produce several images. Thus cr is the
dividing line between ‘weak’ and ‘strong’
gravitational lenses.
Strong Gravitational Lensing
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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
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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
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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
4GM d S  d L
E 
c2 dS d L
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During a microlensing event, the brightness of the source is amplified by an
amplification factor A, given by
A u  
●
u2  2
u u2  4
In practice, source size effects set a limit to how large an amplification can
occur for a very close alignment.
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)
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Planet hunting
Strong and Weak Lensing
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
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
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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
Planet hunting
Planets in orbit around
microlensing stars cause
telltale distortions in the
source star's light curve
OGLE 2005-BLG-390Lb