From: mock@space.mit.edu (Patrick C. Mock)
Subject: Re: grav lensing
Originator: mock@benz
Reply-To: mock@space.mit.edu (Patrick C. Mock)
Organization: MIT Center for Space Research
Distribution: na,sci
Date: Thu, 30 Jul 1992 05:14:35 GMT


(Repost, the first did not appear here.)

Again I must dispute some key points but first ...

In article <Bs647z.Hs5@well.sf.ca.us>, metares@well.sf.ca.us (Tom Van Flandern) writes:
> 
> and mock@space.mit.edu (Patrick C. Mock) and annis@hale.ifa.hawaii.edu (James
> Annis) have patiently disputed this argument.

 ... my compliments also.  I've enjoyed the exchange.

>      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.

This is true only for the case of a lens due to a point mass.  Most
gravitational lenses are due to a galaxy or a cluster of galaxies.
In GR the lens properties depend on the mass distribution of the lens.
An elliptical mass distribution forms an elliptical lens. 
Again I must refer you to Blandford et al (Science 245, 824).  
The relevant discussion is on p 828.  When the source is in the three image
region of the lens, "The images are typically at different distance from the
lens center and are not collinear with it."

>  ... stuff deleted ...
> 
>      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.

No, Palmer's argument does not preclude multiple images because it is
only valid for a point mass.
 
>      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.
> 

The these are seen.  For an examples of a ring see Langston et al, 
Nature (344, 43) and of an arc see Blandford et al, Science (245, 824, 
the arc is show on p 827.)  See Article: 24704 of sci.astro 
From: annis@hale.ifa.hawaii.edu (James Annis) for a discussion of the 
current rates of discovery.

> 
> 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|-
>

One can also get images at saddle points of the time delay in the
image plane.  See Blandford et al, Figure 4.  Again, Fermat's
principle requires a stationary point, which can be a minimum, a
maximum, or a saddle point.  Multiple images are allowed as discussed
above.

A gravitational lens, formed by a galaxy, is an approximately
elliptical lens.  I once attended a colloquium where the speaker
generated multiple images, arcs, and rings with an elliptical lens
made of glass.  It was a very convincing demonstration of the
properties of elliptical lenses.  

Pat