From: metares@well.sf.ca.us (Tom Van Flandern)
Subject: Re: grav lensing
Organization: Whole Earth 'Lectronic Link
Distribution: na,sci
Date: Sun, 26 Jul 1992 20:58:27 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.
>>
>>      But if there is such a point in every direction on the sky around the
>> galaxy, it follows that all point sources produce ring images (perhaps
>> highly non-circular, but rings nonetheless).  But only the rays with
>> modest bending and minimal absorption get magnified and are seen by us.
>> If the source is well off-axis, the ring portion which takes the long path
>> around the galaxy will be much fainter and more absorbed, rendering it
>> invisible.  Hence, a ring arc is the most common type of gravitational
>> lens image.  In the case of galaxies in clusters lensing background
>> objects, it is the only type of image we actually see.

and mock@space.mit.edu (Patrick C. Mock) replied:

> While seemingly plausible, the above explanation is wrong.  The flaw in the
> above argument is that every possible path will contribute to the observed
> image.  Gravitational lenses obey Fermat's principle, which states that of
> all possible null paths from source to observer, the actual light paths are
> those for which the travel time is stationary with respect to infinitesimal
> changes in the path.  These stationary paths correspond to specific points
> in the image plane.  This is very thoroughly explained by Blandford et al.
> Science (Vol 245, pg 824).  Also see Bourassa and Kantowski, ApJ 195:13;
> Gravitational Lenses, Chapter III, QC857.5.G73 1988, and references
> therein.  I don't believe all of these authors have gotten it wrong.
>
> In all fairness, if a point source is perfectly aligned with the cusp of a
> caustic it will be reimaged as an arc but such a perfect alignment will be
> extremely rare.

     I had Blandford's paper in front of me when I wrote my post.  Bourassa &
Kantowski in the paper you cite discuss the case of lensing *through* a mass,
not around it.  Even then, they trace single rays back from the source, which
suppresses information about image shape.  The Gravitational Lenses book
seems to be a review of the preceding, adding nothing new.

     You say you don't believe all those authors got it wrong.  That may be
at the root of this difference of viewpoint, because it has been my
experience that any number of experts who are working toward or expecting a
particular result can fool themselves into that result.  You may notice that
many of the ideas I challenge are held by a pool of "leading experts".  They
must nonetheless be able to withstand critical scrutiny.  It is still my
opinion that the present idea cannot withstand such scrutiny.

     My argument is simple and easy for anyone to grasp.  The counter-
arguments you have quoted require considerable work to grasp even the
essentials, and then they seem so skirt the basic point I have made here: the
*shape* of the image of a point source being gravitationally lensed will be a
ring-arc in general, or a full ring if axial alignment is quite close.
Moreover, that is what is observed in the only cases which everyone here
agrees are true gravitational lenses, namely galactic clusters lensing
background blue objects.

> According to Fermat's principle only null paths for which the travel time
> is stationary with respect to infinitesimal changes in the path contribute
> to the observed image.  For more information on Fermat's principle and how
> it applies to lenses in general, consult Born and Wolf, "Principles of
> Optics", QC355.B736, or your favorite classic optics text.

     I have not yet had the opportunity to refresh myself on Fermat's
principle.  But my recollection is that this refers to the obvious problem
that if a ray path is delayed by one-half wavelength, one gets destructive
interference and hence no image.  Obviously this has no applicability
whatever to the present problem, where ray paths can differ by 10^25
wavelengths.  And it was not invoked in the papers you cited.  If I am mis-
recalling the importance of the principle, please outline the correct general
argument, and I'll complete my refresh on it ASAP.  -|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.