Why does the Einstein cross not form a complete Einstein ring?

[Jorrie]

The Einstein cross (G2237+030) shows 4 reasonably symmetrically spaced images of the very distant quasar, indicating that our alignment with the galactic nucleus to quasar line is fairly good.

How is that it does not show an Einstein ring instead of the cross?

 

[George Jones]

How is that it does not show an Einstein ring instead of the cross?

I think that a ring occurs only for perfect alignment.

A sperical point lens for which the alignment is almost (but not quite) perfect produces two images. Hartle has a nice treatment of the images shapes in this case.

If the lens is a not a point (very small) sphere, e.g., an extended ellipsoidal object, more than two images can be produced.

 

[Jorrie]

Thanks George!

 

[Chris Hillman]

Ditto George, but I add a link to The World's Greatest GTR Simulation!http://www.iam.ubc.ca/~newbury/lenses/lenses.html
Here you can play with your heart's content, producing Einstein rings, Einstein crosses, arcs, and so on, by moving around the background object being lensed, wrt the foreground galaxy.

At the site mentioned in my sig you can find other simulations which I have some reason to think are not entirely incorrect. Caution is advised in all other cases!