One example of the effect of a gravitational lens is
an "Einstein Cross". The picture below shows the objects
2237+0305: a galaxy located in front of a quasar.
The image of the quasar is deflected into four distinct images surrounding the central galaxy core. The question is: how can this happen?
The Einstein cross is intriguing because a mass
having a spherical symmetry can only give rise to images aligned
with the lensing galaxy. If the mass is concentrated in a
small volume, only two images are produced by the gravitational
lens (and if the quasar is centered on the lensing mass, a ring
appears). The following Figure shows what happens:
A ray of light emitted by a source S is indicated by the blue line. The ray is bent at point I by the mass M and reaches point E. The points S, M and O are in the plane of the Figure, but points I and E may be located outside the plane SMO. The vectors and are parallel to each other but point in opposite directions. The angle of deviation is given by the equation .
For the observer O to see the source, the point E must coincide with O. The observer will see the source shifted by the angle d (the direction ). This can only happen if and are in the plane SMO. Then, is also in the same plane. Therefore, the observer can only see an image of the source S located somewhere on the y axis. Careful examination of the equation shows that there are only two solutions, producing an image of S on either side of the mass M.
This may explain two of the four images of the
quasar in the Einstein cross. However, for most cases of
gravitational lensing, the object which serves as the lens is not
a point mass. This explains the other images of the quasar
on object 2237+0305, but the lens would need to have a very
complex shape that is not apparent on the picture.
More information is available on more complex mass distributions producing gravitational lensing. The web page http://leo.astronomy.cz/grlens/grl0.html: Gravitational Lensing With Adobe Photoshop, gives many links to web pages. Also, Chapter 1 in the thesis http://dspace.mit.edu/bitstream/handle/1721.1/40925/212407776.pdf?sequence=1 discusses some important points in the calculation of gravitational lensing.
The question about the mass distribution of the lensing
galaxy of the Einstein cross is discussed in a paper at http://arxiv.org/abs/0807.4175.
This paper answers the following questions:
- What is the mass distribution that can give such a cross? (An oval (quadrupole) mass
distribution (such as the bulge of a galaxy) typically produces
- Why is the mass distribution of the visible part of the galaxy so symmetric?
- Is there more than one galaxy in front of the quasar?
In his book "Seeing Red", Halton Arp expresses some
concerns about 2237+0305 which are:
October 1999, second edition November 2007, third
edition January 2013.