From: metares@well.sf.ca.us (Tom Van Flandern)
Subject: Re: grav lensing
Organization: Whole Earth 'Lectronic Link
Date: Thu, 20 Aug 1992 02:37:57 GMT


     I guess we are making some progress here.  Pat has persuaded me that a
gravitational lens is more like a convex lens than a concave one.  And I
infer that he is no longer questioning the principle that, for a symmetric
lens, source, image, observer, and lens axis must be co-planar.  But these
are side issues to the main questions in this thread:  Of the three classes
of hypothetical gravitational lenses [multiple quasar images, radio rings,
and ring arcs in galaxy clusters], which are true gravitational lenses, and
which are due to some other cause?  I have presented multiple lines of
evidence that the first two are "other", but Pat has argued that this
evidence is not conclusive.  The following points still need discussion:

Earlier, I wrote:

>> 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.

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

> 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.

     One of the first lenses found, the "Einstein cross", has a > 6 magnitude
difference for the missing central image.  This probably has rather low
overall probability.  But one of my complaints about the whole standard model
is its lack of falsifiability.  Nobody bothers anymore to make predictions,
the falsification of which would invalidate the model.  Here is an
opportunity to address that complaint for at least this one aspect.

     Construct a 2-argument table, x vs. y.  Let x be the number of
gravitational lens candidates discovered to date.  Let y be the percentage of
x with a more-than-2-magnitude component brightness difference required to
falsify the hypothesis that almost all such cases are gravitational lenses,
rather than some other mechanism.  Assuming gravitational lens candidates
will continue to be discovered at an increasing rate, a reasonable table
should be able to falsify the hypothesis within a decade, perhaps far less,
if some other mechanism really is dominant; and conversely.

     Can you construct such a table?  If not, who could?

>>>> 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?

     Instead of the abstract phrase, "stretching the theory", let me
substitute, "introducing a new 'ex post facto' hypothesis which does not
automatically follow from the original model, solely for the purpose of
insuring continued agreement with observational constraints."  IMO, when this
becomes necessary, it is a dead giveaway of a model which is fundamentally
wrong.

     You may argue that this new, complicated variant of the microlensing
theory does automatically follow from the original model.  But one cannot
make specific, quantitative, statistical predictions of the rough amplitude
and frequency of microvariability.  Instead, one derives lensing galaxy mass
density parameters which make the hypothesis work, invoking dark matter where
needed.  No a priori constraints are placed on plausible values for the
derived parameters, even when M/L values come out quite large.  Using such an
approach guarantees that even a totally wrong model will appear to be
working.  -|Tom|-

-- 
Tom Van Flandern / Washington, DC / metares@well.sf.ca.us
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