From: metares@well.sf.ca.us (Tom Van Flandern)
Newsgroups: sci.astro
Subject: Re: grav lensing
Date: 16 Aug 92 16:36:36 GMT
Distribution: na,sci
Organization: Whole Earth 'Lectronic Link


Earlier, I wrote:

>> An ordinary convex lens produces no bending of the light path through its
>> center, but ever increasing amounts of bending for light paths farther and
>> farther from the axis.  This is why it can focus light to an image at a
>> specific distance.  On the other hand, a {concave} lens produces no
>> bending on axis, reaches a maximum bending at some angle, then has less
>> and less bending approaching zero again.  Gravitational lenses behave
>> qualitatively in the latter fashion, because the strength of the
>> gravitational field decreases as one moves away from the lensing galaxy.
>> That is why both of these lens types (gravitational and concave) produce
>> rings or ring arcs from extended sources, unlike convex lenses.

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

> This explanation is also wrong.  For example the sun acts as weak convex
> lens.  In a classic test of GR, the apparent images of stars observed near
> the sun during a solar eclipse are displaced away from the sun's center of
> mass as they would if a giant convex lens replaced the sun.  This happens
> because the sun or a convex lens deflects the light rays slightly inward so
> the apparent images move slightly outward.  A concave lens would have the
> opposite effect.

     We are focusing :-) on different properties.  What you say is true, but
it did not invalidate what I said.  I was contrasting gravitational lenses
with the convex lens's ability to focus rays to a point, forming an image
which gravitational lenses cannot do.  I was comparing gravitational lenses
with the concave lens's zero-to-maximum-to-zero bending pattern as one moves
away from the axis.  For convex lenses, the bending just keeps getting
greater as one moves away from the axis, which is certainly not the case for
gravitational lenses.  So for purposes of my analogy, concave lenses behave
more like gravitational lenses.

> A correct way to understand the properties of a lens is to look at the time
> delay through various parts of the lens (see The Feynman Lectures I, Ch
> 26).  For a glass lens the time delay is proportional to it's thickness and
> index of refraction.  A convex glass lens will have a maximum time delay at
> it center which decreases to zero at the edges.  A concave lens has a
> minimum time delay at it center and the time delay increases toward the
> edge of lens.  The time delay for a gravitational lens is at maximum where
> the potential is deepest.  Therefore, a convex mass distribution will
> generate a convex lens!

     Can you say in a few words why this time delay is relevant?  Simple ray
tracing seems more to the point here.

> Why do you object to the theory in the case of point sources but not
> extended sources?

     Extended sources can be treated as an assembly of point sources.  For a
*symmetric lens*, one should clearly not get qualitatively different
phenomena for a single point source and for multiple point (extended)
sources.

>> The number of lensed images is not consistent with theory.  Caustics
>> should separate the image plane into odd numbers of images; but even
>> numbers are more often seen than odd numbers.

> The standard theory also predicts that the relative magnification will vary
> widely.  The magnification of a true point source on a caustic line is
> infinite, so variation of several orders of magnitude are not surprising.
> In the simple elliptical lens model one image is always significantly
> fainter than the others so an even number images is not surprising.

     Since you bring up this argument, let me mention Kassiola & Kovner, ApJ
388, 33 (1992).  They show that the frequency of occurrence of multiple
quasar images with large magnitude difference (3 of 14 cases have more than a
two magnitude difference) exceeds the theoretical upper bound for such large
differences in the lensing model.  This is assumed to be an artifact of small
number statistics. However it is more difficult to discover large-magnitude-
difference cases, so the discrepancy is in the wrong sense to save the
theory.

>> Wambsganss (ApJ 392, pp. 424-431, 1992) showed that microlensing cannot be
>> due to individual stars, but must be due to crossing caustics of the lens.
>> The lensing model just keeps getting weirder.

> The complicated nature of his results do not justify calling them weird.

     Choose your own adjective.  I was pointing out how much stretching is
going on among theoreticians to save the lensing theory.  -|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.