From: metares@well.sf.ca.us (Tom Van Flandern)
Subject: Re: grav lensing
Organization: Whole Earth 'Lectronic Link
Distribution: na,sci
Date: Wed, 29 Jul 1992 20:43:11 GMT


Earlier, I wrote:

>> Point sources do *not* (and almost *cannot*) be imaged by a gravitational
>> lens into another point image.  The almost inevitable image is a ring arc;
>> and rather rarely, a complete ring.
>>
>> To see this, consider a galaxy acting as a lens for a point source
>> somewhere behind it.  Now trace light rays backwards from our eyes, past
>> the galaxy, to the point source.  You can now see at a glance that, at
>> *every* direction on the sky from the galaxy's center, there will exist a
>> single, unique, angular distance at which the bending will be just right
>> to connect source to observer.  At any greater distance the galaxy's
>> gravity is weaker and the bending less.  At any lesser distance the
>> galaxy's gravity is greater and the bending more.  There is one and only
>> one angular distance at which the bending is just right.

and mock@space.mit.edu (Patrick C. Mock) and annis@hale.ifa.hawaii.edu (James
Annis) have patiently disputed this argument.

     In the meantime I received the following argument via E-mail from
palmer@cco.caltech.edu (David Palmer):

> Suppose that the image forms a ring arc.  Now, take two sources which form
> overlapping ring arcs. Now if the observer fires a beam of light backwards
> along the direction to the region of overlap.  To which source does the
> beam of light go? (It does not split or spray)
>
> You can also see it by recognizing that gravity is a central force, and so
> the image, the source, the mass, and the observer must all lie in the same
> plane (by symmetry and angular momentum considerations.

     To this I replied:

     "Good arguments.  I see the point.  I have been overly influenced by an
analogy with solar eclipses.  As viewed from the Moon, the Sun being eclipsed
by the Earth's atmosphere (an analog of a gravitational lens because of
refraction) first becomes a ring arc, which gets longer and longer until it
is a complete ring.  I now see that the finite size of the solar disc is
crucial to this effect -- a point I did not appreciate before.  Some elements
of my original argument about quasars still survive.  But I now see that
point sources can get lensed into point sources.  [I should have realized it
from stars photographed near the Sun to test for the GR light-bending effect,
which remain point images!]"

     As this pertains to the original point, it means that lensed quasars do
not have to be ring arcs as long as the quasars are not resolved.  But the
same argument also precludes multiple quasar images.  So my paragraph of
objections to gravitationally-lensed quasars still stands.

     As for the discussion of lensing of radio lobes, nothing is changed
because those are resolved sources, which should produce ring arcs and rings,
just as we see when galactic clusters lense background blue galaxies.


James Annis then writes:

> Fermat's principle predicts multiple images of a gravitationally lensed
> point source. A point very close to the point source might be lensed into
> an image very close to that of the point source, thereby creating arc
> shapes.  But a point source is a point source; there is not light from "a
> point nearby".

     One can clearly get two images: one where the path is a minimum, and one
on the opposite side of the lens where it is a maximum.  Any other images
would violate Palmer's second argument about the need for the image to be in
the same plane as source, lens center, and observer.  So how do you plan to
explain quasar gravitational lenses this way?  -|Tom|-

-- 
Tom Van Flandern / Washington, DC / metares@well.sf.ca.us
Meta Research was founded to foster research into ideas not otherwise
supported because they conflict with mainstream theories in Astronomy.