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Physics 133: ExtragalacticAstronomy and Cosmology

Lecture 16; February 26 2007

Previously:

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Energy is preserved during the expansion,locally.

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There is dark matter –^

Galaxies – rotation curves

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Clusters – virial theorem and hydrostaticequilibrium

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We do not know what it is: –^

It cannot be hidden baryons

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It could be new exotic particles..

Detecting dark matter. Gravitational

lensing!

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Mass concentrations perturb spacetime, altering thepropagation of light

Detecting dark matter. Strong

gravitational lensing!

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Under special circumstances the distortion is sostrong that creates two images of a backgroundobject. This is called strong lensing

Detecting dark matter. Why is it called lensing?

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The physics is verysimilar to that ofcommon opticallenses

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In fact many of thefeatures ofgravitational lensingcan be reproduced bycommon opticaldevices.

Einstein Ring

Double

Source

Quadruple

Figure courtesy of Phil Marshall

Detecting dark matter.

Strong lensing by clusters

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Clusters are alsostrong lenses

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The blue objects hereare distorted images ofthe same object

Detecting dark matter. Weak lensing •^

Even when thegravitational field is notstrong enough to producemultiple images, the largescale structure perturbsspace time

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This alters the shape ofobserved galaxies in thesky, shearing andmagnifying them in ameasurable way

Detecting dark matter. Weak lensing

mass maps

Optical image

Dark matter mass

Lensing Basics.

I: Thin Screen Approximation

Surface mass density

Deflection angle

For azimuthal symmetry

Reduced deflection angle

Lens equation

Critical density

Lensing Basics.

II: useful general relations

2D potential 2D Poisson Equation^ Jacobian matrix

The time delay surface and

Fermat’s principle

The time delay surface and

Fermat’s principle

Lens equation Extrema of thetime delay surface^ adimensional

Time delay surface^ Multiple images form at the extrema of the time delay surface

Summary. Lensing basics

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Mass concentrations distort the images ofobjects in on the sky in a way similar to thatof optical images.

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Strong and weak lensing provide veryaccurate mass maps of objects (in projection)

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Gravitational fields also “slow down” light.Strong lensing can be formulated in terms ofFermat’s principle

The End

See you on Wednesday!