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
Date: Mon, 17 Aug 1992 01:34:02 GMT


In article <Bt34t0.Iu9@well.sf.ca.us>, metares@well.sf.ca.us (Tom Van Flandern) writes:
> 
>      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.

Concave lenses do not behave more like gravitational lens.  Your analogy
is wrong as follows:

  Clearly a convex lens doesn't bend light once you get beyond the edge of
  the lens, so I'll assume that you are ignoring edge effects.  In this
  context your description of a convex lens is accurate to point.  However,
  you neglect to specify the direction of the bending.  A convex lens bends
  incoming rays TOWARDS the optic axis.  A spherical convex lens will focus
  a parallel beam to a point.  The output beam diverges from a point one
  one focal length in front of the lens.
  
  Your description of a concave lens is wrong.  Again I assume we are
  ignoring edge effects.  A concave lens, like a convex lens, has zero
  bending on axis and increasing bending outward. The bending does not reach
  a maximum and start decreasing again.  A concave lens differs from a
  convex lens in that the bending is AWAY from the optic axis.  A spherical
  concave lens transforms a parallel input beam into a diverging beam that
  appears to originate at a point one focal length behind the lens.

  (Both types of spherical lenses convert a parallel beam into a diverging 
   beam.  Thus they will appear to be similar when the source, lens, and 
   observer are sufficiently far apart.)
  
  If we now consider the edge effects, both types of lenses have a
  zero-to-maximum-to-zero bending pattern.  So a gravitational lens
  must also has a zero-to-maximum-to-zero bending pattern.  The important
  point is that a gravitational lens formed by a convex mass distribution
  bends light TOWARDS the optic axis.  Therefore it is a convex lens.
  
  (The edge effects can be made smooth or sharp for both types of 
   lenses by varying the construction of the edge of the lens.)
  
>      Can you say in a few words why this time delay is relevant?  Simple ray
> tracing seems more to the point here.

Ray tracing is never as simple as it seems.  It only identifies null paths
through the optical system.  You still have to rely on Fermat's principle to
determine if that null path is actually used.  Ray tracing is most useful is
relatively simple optical systems in which all null paths are stationary.

The time delay approach is important because light always follows a path with
stationary time delay.  This is a basic principle of optics.  Feynman give a
good explanations of this in Vol I, Ch 26 and in his book "QED, The Strange
Theory of Light and Matter".  Ch 26 is only 8 pages.  I encourage you
to read it.

> > 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.

No this is not true.  If I take a picture of a star next to a galaxy at two
different magnifications, the size of the galaxy and the separation of the
star and galaxy will scale with the magnification but the size of the star (a
point source) will remain the same.  

More precisely the size of the stellar image scales with the resolution of
the optics but for a large telescope the resolution is determined by the
atmosphere and not the magnification.  An extended source can be treated
as an assembly of point sources only if you are careful.

Furthermore, most galaxies have elliptical mass distributions.  Your claim
(to James Annis) of what ought to be:

>   A single galaxy lens ought to be sufficiently symmetrical to qualify
>   in this respect at any orientation.  (The s-l-o plane model is true.) 

is not correct.  For example, Blandford et al explicitly state that the
elliptical asymmetry is essential to get the multiple images.  They also
show models of single galaxy lenses based on observations that have
multiple images and show the lensing galaxy.  The single galaxy lens
derived from the observed galaxy is asymmetric.  Other similar examples
are in the book "Gravitational Lenses".

>      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.

Quoting from Kassiola & Kovner (section 5, Discussion): 
"These frequencies, however are derived from estimates of magnitudes in a
very small set of lens candidates.  For this reason the uncertainties of the
points in Figure 1 are very large ( we do not even show them in the graph)."

This implies that the measurements are consistent with the theory within the
current errors.  They also point out that reasonable changes in their
assumptions concerning the intrinsic quasar counts would increase
the expected number of large magnitude differences.  Their point
that much more data is needed is the most important.

> 
> >> 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|-
> 

IMHO Wambsganss is not stretching the theory.  He is applying the standard
theory of gravitational lenses, GR and standard optics, to a more complicated
system.  The standard theory tells us that the behavior of a gravitational
lens is governed by the mass distribution.  Treating a galaxy as a smooth
elliptical mass distribution is only an approximation.  A galaxy is a mixture
of stars, gas, dust, etc.  His work looks at the microlensing effects of
ensembles of stars.  He shows that these effects are important in understanding
the fine details of the caustics of a gravitational lens formed by a galaxy.
How is this stretching the theory?

Pat

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