Is There a Common Pattern in Einstein Crosses?

[Buckethead]

TL;DR Summary

common pattern emerges from Einstein Cross

This is probably just a coincidence, but I happened to notice while looking at Einstein crosses an unusual pattern common to these four images. I was looking for more but it turns out there may not be as many crosses as I originally thought. Must be rare. The pattern is that of the 4 background objects (quasar, supernova) the line connecting two of them cross the center, while the line connecting the other two are offset from the center. Also, I'm fascinated by the symmetry of the two pairs in the images. The first observation is likely a fluke but the symmetry is what kind of gets me. For what must be an obviously distorted lens, it's a bit strange that there would be not only symmetry of one pair, but of two pair! In other words, it would be much more likely to see a two object image around the center (not even pairs, but just in two random locations) than to see two perfectly symmetrical pairs. Comments?

 

[anuttarasammyak]

Fermat’s principle says stationary angles as for time to arrive come true. I am not qualified to tell more but I suppose four cross points represent maximum, minimum and two inflection points.

 

[sophiecentaur]

Fermat’s principle says stationary angles as for time to arrive come true. I am not qualified to tell more but I suppose four cross points represent maximum, minimum and two inflection points.

What selects the orientation of the cross? I might have expected a ring (??).

 

[Ibix]

What selects the orientation of the cross? I might have expected a ring (??).

The Wikipedia page on Einstein crosses notes that it's due to the highly elongated shape of the galaxy doing the lensing.

 

[sophiecentaur]

Good answer!

 

[Psnarf]

An elliptic lens has two foci. Photons from one distant galaxy passing through the gravitational lens of two merging galaxies forming an ellipse with a super-massive black hole at each focus could produce two of the points of the cross. What could produce the other two? Another dual black hole elliptical galaxy with a major axis perpendicular to the first? Do subsequent observations of an Einstein Cross show any motion of the foci as the galaxies merge?

 

[Ibix]

An elliptic lens has two foci. Photons from one distant galaxy passing through the gravitational lens of two merging galaxies forming an ellipse with a super-massive black hole at each focus could produce two of the points of the cross.

You get two points from a spherically symmetric lens. Essentially this comes from light passing "over" and "under" the lens. They will smear into a ring as the source passes behind the lens. This behaviour has to happen because orbits about a spherically symmetric mass must lie in a plane, and it must be the plane defined by the source, the lens, and the observer. This plane is only non-unique when all three are colinear.

If the lens is non-symmetric, apparently you can get a cross pattern. I don't know any way to deduce this without numerical modelling, but I can't see why two interacting elongated sources would be necessary.