Starship Asterisk*

What an incredible coincidence, the quasar being positioned so precisely behind the center of the lens galaxy!

I find it interesting that the cross is caused by the galaxy as a whole, and yet noticeable changes in brightness are observed as stars from the lens galaxy transit the quasar. I would have thought the two effects would be way out of proportion!

The most recent APOD on the Einstein Cross (APOD 2007 March 11) revided some thoughts of mine on a preceding APOD on a Polar Ring Galaxy.

Via APOD 2007 February 16 on a polar ring galaxy I was linked to another relevant web site, which indeed is very fascinating - not the least by the animated simulation of its Fig.3.

http://www.obspm.fr/actual/nouvelle/apr03/prg.en.shtml

It did not take me long to remind me of an earlier question, which I could not get answered before, even by an expert. - What strange mass distribution in a gravitational lens could possibly create the spectacular Einstein Cross?
>> http://antwrp.gsfc.nasa.gov/apod/ap001010.html <<

Clearly enough, it does not require much mathematical insight to conceive that an elliptical mass distribution in the lens cannot create the almost symmetrical quadruplex image of a clover leaf. Yet, two disks overlapping at an angle probably could. The simulation of Fig.3 (Bournaud & Combes) convincingly displays how such a configuration can be achieved. Hence, I should like to rephrase my original question as follows. - Could a polar ring galaxy be the lensing mass for the Einstein Cross?
Actually there is some warp to be seen in the faint image of the lensing galaxy in question (as cited above, and shown anew by APOD 2007 March 11), although by far not as spectecular as in the simulation of Fig. 3 (Bournaud & Combes).

Would it perhaps be possible to feed the results of the preceding modelling into the numerical modelling of the expected image of a quasar that is assumed to be perfectly aligned behind that lens? It should be helpful to assume a large source to lense ratio of ~10, concerning the respective distances to the observer (as cited in Cumming & DeRobertis 1995, PASP 107:469-473).
>> http://articles.adsabs.harvard.edu/cgi- ... .107..469C <<

Has a similar study ever been performed before? - If not, it should really be interesting to try.

I hadn't thought of that. So this could be a possible solution as to why we end up seeing a cross shape (four distinct images of the quasar) instead of a ring of light as the quasar is lensed around the galaxy? And why it is lensed at four distinct angles instead of every angle. I haven't looked at your links yet. I'll do that now.

About the lensing. . . I wonder if the galaxy will lens specific wavelengths differently. Do all images of the quasar, from radio signals to Xrays achieve this so-called cross shape?

I realize that the theory states that it is the gravitational field that causes the lensing, so the gravitation field does not change with each wavelength that passes through. But it could bend it differently.

Richard Egel wrote:
It did not take me long to remind me of an earlier question, which I could not get answered before, even by an expert. - What strange mass distribution in a gravitational lens could possibly create the spectacular Einstein Cross?
>> http://antwrp.gsfc.nasa.gov/apod/ap001010.html <<

Clearly enough, it does not require much mathematical insight to conceive that an elliptical mass distribution in the lens cannot create the almost symmetrical quadruplex image of a clover leaf.

It appears that the cloverleaf shape is the result of near-perfect alignment with an elliptical mass distribution. See here:
http://www.iam.ubc.ca/~newbury/lenses/mfk/mfk.html

this question might be very significant

Just for grins I retrieved a set of Hubble exposures of this object and processed them into an image. It's a little closer view of the Einstein Cross, though not exposed quite so deeply as the APOD. The galaxy core is easier to see here.

Enjoy.



-Noel

It appears that there is also some slight spiral architecture visible at the top and bottom

If anyone is watching this post I would be grateful for a little help with this image and others that show no evidence of Einstein's Rings, but are still attributed to gravitational lensing.

To digress. A conventional lens (i.e. an imaging lense) differs from a gravitational lens in one very important way, curvature increases away from the lense axis rather than towards it. This means that a gravitational lens has no single focus and is why Einstein (correctly as usual) considered that such a 'lens' would image an object lying directly behind the 'lens' as a ring (if you could move closer the ring would grow larger, and moving away would make it smaller). Einstein (again correctly) considered that such a perfect alignment would be so fortuitous that it was unlikely that it would ever be observed. He made no mention of multiple 'optical lens'-like images as seen in the feature that bears his name - I wonder how he missed that?

In fact, because of the HST's phenominal success, there have been many photos showing partial and even complete examples of Einstein's rings, the partials due to a very slight off-axis viewpoint. What characterises all these is the distorted annular 'lensed images', in complete contrast to the undistorted objects in the Einstein Cross. If Einstein's rings prove gravitational lensing then why are there not even partial rings in this image.

I'm thinking the quasar is as close as one can get to a true point light source, and is not on-axis to make a ring, and the material in the quasar's surrounding galaxy (assuming there is one) isn't light enough to show in these images at this exposure depth. The rings seen in other Hubble images are of entire galaxies stretched out, not of point light sources.

I'm also thinking the gravitational lens probably isn't optically perfect, but is affected somewhat by the non-uniform local density of the mass in the intervening galaxy.

-Noel

Hi Noel,

Thanks for the quick response.

My thinking was this;

If a quasar is considered a point source by virtue of its distance from the lens, and if the gravitational lens is 'simple', and if the observer, lens, and quasar are aligned, then there is only a single 'null geodesic' lightpath that connects quasar and observer in any plane bounded by the axis (two symmetrically about the axis in the plane containing the axis). It is the rotational symmetry of this single null geodesic about the axis that produces a unique cone of light (unique to the observer) that is the phenomena of Einstein's Rings.

It is because the gravitational lens is, in fact, an 'anti'-lens in that it causes greater 'bending' of light passing closer to the center of the lens, that no focusing of light from a point source can occur, and the ring seen will vary in size as the observer moves along the axis. A corollary is that no brightening of a point source can occur.

Focusing will occur within the ring where the 'quasar' is not a point source but rather a disk as there will be many 'unique' null geodesics linking the different parts of the disk to the observer through the lens. But no inversion of the image would occur - the 'sidedness' of the ring matching that of the 'quasar' it images.

However I look at it, a simple gravitational lens will not produce multiple undistorted images to an observer.

If the gravitational lens is complex (like an 'anti' flemish glass for instance) then complex 'rings' would result and where they intersected could give the appearance of multiple images (the 'clover leaf'?) but since the intersecting would only double the luminosity it is difficult to believe that the 'half' luminosity rings cannot be detected.

Very interesting thoughts.

I frankly hadn't considered the lens in any sort of detail in my mind. My thinking was simply that with SOME level of complexity in the lens the light could end up taking four discrete paths through time/space to end up here, and within those paths some focusing might occur, which would explain the quite obvious brightness differences.

There's a link up in this thread posted by norup to a simulation that shows how a cross could show... Or at least how a ring with 4 brighter parts could show. You're right, though... No ring like structure appears in the actual images, at least not at the resolution/depth shown.

-Noel

Could it be that there are four massive gravity wells located at the center of the foreground galaxy, each in turn skewing the light from the source into four seperate paths? Further, given different relative densities of those four massive central objects, could they not bend different relative ammounts of light toward our perspective to cause the viewed image?

I keep coming back to the fact that a gravitational lens does not act like any optical lens or lens system, and that using the term lens only serves to confuse any debate.

An optical lens system can produce multiple images because, in the simplest case of a fractured lens where each fragment has a suffered a slight mislignment of the original axis, each fragment casts an image identical to that cast by the unfractured lens, but each in a slightly different place.

In a simple (spherical) gravitational lens the original 'image' is a ring (or part thereof), never a 'likeness' of the source, as the result of the rotation about the axis of the unique null geodesic. And if there exist ellipsoidal gravitational lenses, the shape of the null geodesic will change systematically around the axis to produce an elliptical ring widest where the curvature of space/time is greatest. But it will still be a ring even if a deformed one, and if quasar, lens, and observer are coaxial it will be a complete one.

It may prove, with technological improvements, that the elements of Einstein's Cross are indeed intersections of annular images, but as the images stand, for the Einstein's Cross to be produced by gravitational lensing, gravitational lenses must behave like conventional lenses and Einstein (and all those HST photos) must be wrong. Fortunately he isn't and there must be some other explanation for the Cross.

Occams razor would suggest that there are four quasars, but the images indicate that two (east and south) are brighter and possibly in front of the central low redshift object, while the other two (north and west) are dimmer and possibly behind it. - Which is why, I guess, that there is so much effort being made to discredit Occam.
And so much pretence that gravitational lenses behave like optical lenses.

Steve

Perhaps a better, and possibly more descriptive term should be gravitational refraction rather than gravitational lensing.

Hm, I'm not sure I fully agree with everything you're saying, brachiopod. I don't mean to be argumentative, but...

Why can't gravitational refraction - bending of light rays - be compared to a physical lens? Can there not be made a physical (e.g., glass) structure that bends light in the same manner as a gravity field? Maybe it's not going to look like a simple convex lens, but nonetheless some kind of plate with curved surfaces, quite likely complex?

Einstein (and all those HST photos) must be wrong

Hm... Perhaps you haven't looked closely enough at the Hubble images.

Regarding there never being a likeness of the object in the background... That statement seems to go against observed reality. Consider the images on the web pages below. I see a lot of distorted galaxies in the background, and even some that look doubled or tripled. Thin, stretched, curved, yes, but still reminiscent of galaxies. Any one brilliant point light source in those galaxies would indeed show as one or more point light sources, just as we see in Einstein's Cross. With sufficiently high magnification it might resolve into a stretched disk, but we don't have such magnification at our disposal.

http://www.spacetelescope.org/images/html/opo9610a.html
http://www.spacetelescope.org/images/ht ... 0404a.html
http://www.spacetelescope.org/images/html/opo0301a.html

Just think about it... At some vector in space you have a clear shot (no gravitational lensing) and at another you have intervening mass (causing gravitational lensing). There's not an abrupt transition between the two, but rather a gradual changing in the distortion of the image of the background objects, from unstretched to slightly stretched, to extremely stretched.

Another way to look at it... Light rays emanating from a distant object radiate in all directions. Some of those rays that make a cone shape with us at the center. The gravity from intervening mass distorts the trajectory of some of those rays so as to cause them to bend toward us. If done perfectly, we'd see a point light source distorted into ring. If the distortion is slightly imperfect because of an uneven distribution of mass, we may see a number of separate objects. I don't find this hard to imagine at all.

-Noel

Hi Noel,

On the lens issue, (leaving aside that the physics is totally different as far as I have read), a glass medium analog of a simple gravitational lens would be a lens that was flat furthest from the center that increased in curvature towards the center until it reached a peak at the center (actually two peaks symmetrically either side of the lens along the axis as the lens would be symmetrical about a plane orthogonal to the axis) . In the case of a 'black hole' the gradient at the center would be infinite I presume.

[As I mentioned earlier, switching the internal and external elements along a transverse section through a fresnel lens would produce a similar effect.]

You are quite right in surmising that I haven't had the opportunity to look at enough Hubble photos, but I have tried to look at as many as I could of those purporting to show the effects of gravitational lensing (including those you included the links to, thanks for those).

The problem I have with those I have seen is reconciling Einstein's analysis of the effect of viewing luminous objects that lie behind a gravitational mass - i.e. Einstein's Rings (arcs of distorted images) - and explanations that invoke the same mechanism to explain the observation of multiple 'undistorted' images.

In short my problem is not with the photos that show the phenomena Einstein expected, but with those that seek to explain other phenomena by the same physics. [As an example of political spin they could do no better than name after Einstein the non-Einsteinian example (in the sense that it doesn't exhibit his predicted phenomena) that sparked this thread.]

I do apologise for not clarifying what I meant when I used the term likeness I knew it would lead to problems. By likeness I meant a scale independent facsimile rotated or otherwise, not something that might, on balance and after careful consideration, be identified as one object rather than another - a passport photo rather than the Turin shroud.

As to the often stated ability of a gravitational lens to produce multiple 'undistorted, non-arc' images, I cannot visualise this in terms the null geodesics linking source and observer via a single 'dimple' in space time. The best I can see is that the source can be seen directly and undistorted (not through the lens) at the same time as it can be seen through the lens as a distorted partial arc of an image. To see more undistorted 'images' requires more sources not more lenses.

Perhaps I have just not grasped the idea of caustics as applied to gravitational lenses rather than teacups.

Thanks for your ideas.

Steve

I've always assumed scientists identified the 4 bright quasars in the Einstein Cross as one by comparing their spectra.

Some interesting tidbits of information at these links:

"Special cases" of gravitational lensing mentioned here:
http://www.gemini.edu/index.php?option= ... view&id=78

Something about the use of spectra here:
http://spot.pcc.edu/~mhutson/astronomy/ ... 042005.htm

Some pretty detailed analysis of spectra and also revealing possibly a 5th component is here:
http://www.astro.psu.edu/users/xdai/head2002.pdf

And finally, some dissenting opinion here:
http://laserstars.org/references/lenses.html

-Noel

Many thanks for the links Noel, I am ploughing my way through http://xxx.lanl.gov/abs/astro-ph/9912508 on Weak Gravitational Lensing which seems to be how multiple images are formed rather than rings and arcs.

It seems that Einstein's Cross is getting a great deal of telescope time so maybe I can return to the thread later.

Steve