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ASTR 200 : Lecture 26

Gravitational Lensing

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Announcements

• HW 7 due tomorrow

– Office hours today and tomorrow posted

• HW 8 distributed Friday Nov 10, due Thurs Nov 16

• Final examination on Thursday Dec 7, 8:30 AM

– Location not yet published

– Formula sheet will be provided in advance

– Will be cumulative

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The 'Mass to Light' ratio

• Important simple quantity used in discussions of galaxy dynamics and dark matter.

• The Mass-to-Light ratio of an object (examples: a star cluster, a galaxy, a cluster of galaxies) is just the estimated mass (in solar masses) divided by amount of energy output, in solar luminosities.

• Thus, by definition the M/L ratio of the Sun is 1.

• The M/L ratio of the Solar System is just slightly bigger than one

• Globular star clusters have M/L ratios of 1-3

• Typical galaxies have M/L ratios of 2-10.

– Expect M/L > 1 because most stars have M<1 and L<<1

– However, even a few high-mass stars add lots of light, bringing the M/L down

• Typical galaxy clusters have M/L in the range 10-100.

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If mass produces acceleration, light could be lensed

• Remember that

and so in Newtonian physics, acceleration is independent of mass of the object being accelerated (Galileo with cannonballs and grapes)

• Even in the 18th century, based on Newton's belief that light was made of particles, people realized that if light skimmed past the Sun, there would be an angular deflection, with an angle of 0.85”

• The effect would be to make the star appear to shift away from the Sun

m a=GMm

r2 → a=GM

r2

● Of course, the issue is that it is difficult to see background stars behind the Sun...

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But, during a solar eclipse...

The bending falls off if the light path is further from the Sun

­But there was no way to make the measurement.­ Couldn't look through a telescope and see 1” deviation

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General Relativity made a DIFFERENT prediction

• GR predicts a deflection angle

where b is the impact parameter – the distance between the photon and the center of the mass at closest approach along the path (see diagram)

• For the Sun, a skimming path is deflected by ~1.7'' , which is twice the Newtonian expectation

α≈1b

4 GM

c2

● This was a 1915 prediction of GR that was different than Newtonian physics, and so testing it (which had now become possible due to the invention of  photographic plates) was the subject of an expedition to a solar eclipse in Africa in 1919 

b

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GR : 1Newtonian : 0

This was the only detection of gravitational lensing for a long

time...

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The general approach: The lens equation

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The general approach: The lens equation

DS

(Must have dimensions  of length squared)

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The Einstein radius

DS

Suppose source precisely behind the lens. r=0 and then r'=rE and the source 

appears moved by rE. Because configuration symmetric, we see a ring of 

angular radius θE=r E

DS

=√ 4 GM

c2

DLS

DL D s

θE

11The central 'lensing' elliptical galaxy is lensing a background galaxy  ­ Requires nearly perfect alignment of the background object, thus rare

An Einstein Ring

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A collection ofEinstein rings

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Amplification in Lensing

• Lensing magnifies/amplifies the brightness of background sources because more total light is delivered to the observer

• Imagine placing the background object at various places along a line (above) with a given y=b. As a function of x, you get various brightenings (right)

`horizontal'

x

x

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Multiple images in gravitational lensing

• In the realistic case an object is lensed into a finite number of images, with different amplifications and offsets

● The number of images, their amplification, and their position actually probes the mass distribution of the lensing distribution● So, this allows one to(1) see, via amplification, very distant sources(2) probe mass (of lens) using lensing physics

● (independent of dynamics) 

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Gravitational lensing

by clusters of galaxies

● These arcs are commonly seen when looking through massive galaxy clusters 

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Gravitational lensing by clusters of galaxies

● One can model the amount and distribution of mass in the cluster using the image shapes● This probe has no dependence on velocities, etc

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Other types of lensing

● This was all what is called 'strong' gravitational lensing

● We have also discussed● Micro Lensing

●  And there is also 'weak lensing'

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Microlensing

● Previously discussed when taking about the halo● Can also be used to detect exoplanets around the (invisible) lens

● Here the lens is not seen, and there is only 1 image● However, one uses the fact that the geometry of the lens versus source 

is CHANGING due to relative motion, and one is detecting the amplification of the background source in intensity

● This has been used to study populations statistics in the Milky Way halo 

brighter

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Weak lensing

● When light passes a through a low­mass system, a circular cross section has its shape very slightly affected

● If there were only one lensed object, nothing can be learned from weak lensing 

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Weak lensing● This is done statistically using the observed shape of large numbers of galaxies affected by some foreground mass distribution● The are correlations between galaxies on the sky due to the presence of mass in the foreground. This allows detection of mass even if the lens emits no light! 

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Abell 502 : The Bullet Cluster

● A massive cluster which is actually two clusters post a collision 

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Abell 502 : The Bullet Cluster● The Chandra X­ray telescope image shows that the two clusters have passed through each other, leaving especially hot stripped gas between them

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Abell 502 : can be studies by weak lensing● However, most of the mass will be in dark matter.   This can be detected via its weak lensing on background galaxies.  Where does it say the dark matter is?  (see next slide) 

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Abell 502 : Dark matter stays with the galaxies● The weak lensing reconstructed mass distribution (contours) shows that the dark matter `stays with the galaxies' and is not distributed like the hot gas

This shows that the dark matter interacts only gravitationally, and not like the gas

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• Moral: lensing is kewl

The Cheshire Cat lens.

Will disappear over the next Gyr as the two elliptical lens galaxies merge