Symmetry breaking by gravitational lens?
Jeff Baldwin
around such a lens will appear as a symmetric ring instead of bent,
mirrored images on opposite sides of the lens. But the pictures of such
lenses that I have seen invariably show the bent, mirrored type of
"reflection" images and not what I would expect from an isotropic,
symmetric lens. This seems to me to exhibit a type of broken symmetry.
What am I missing?
Thanks! -Jeff Baldwin
[Moderator's note: you'd have to be awfully lucky for the
gravitational lens to perfectly lined up between you and
the galaxy. - jb]
Jeff Baldwin
lens was off-center with the line between me and the galaxy, I'd expect
to see a distortion in the images of the galaxy, one side being smaller
and less distorted than the other. But what is observed is a set of
identical mirror images of a galaxy that seems to me to indicate a
preferred direction of propagation along some axis of some type (a
polarization or something like that?). Is it possible that some sort of
preferred direction or orientation of electromagnetic propagation is
responsible for the types of images observed to bend around gravity
lenses?
Jeff Baldwin <mv...@idt.net> wrote:
>If a gravitational lens is isotropic, then the image of a galaxy bent
>around such a lens will appear as a symmetric ring instead of bent,
>mirrored images on opposite sides of the lens....
Chris Hillman
> you'd have to be awfully lucky for the gravitational lens to perfectly
> lined up between you and the galaxy.
True, but incredibly enough, a rather striking Einstein ring has actually
been observed! See my page
http://www.math.washington.edu/~hillman/Relativity/tests.html#gl
for HST images of this and other lenses, and be sure to play with the
fabulous demo and information available here:
http://www.iam.ubc.ca/~newbury/lenses/lenses.html
Chris Hillman
Home Page: http://www.math.washington.edu/~hillman/
Phillip Helbig
writes:
> Jeff Baldwin <mv...@idt.net> wrote:
> >If a gravitational lens is isotropic, then the image of a galaxy bent
> >around such a lens will appear as a symmetric ring instead of bent,
> >mirrored images on opposite sides of the lens....
> >
> >[Moderator's note: you'd have to be awfully lucky for the
> >gravitational lens to perfectly lined up between you and
> >the galaxy. - jb]
> That's what I thought, too. And that may be correct. But then if the
> lens was off-center with the line between me and the galaxy, I'd expect
> to see a distortion in the images of the galaxy, one side being smaller
> and less distorted than the other.
OK.
> But what is observed
You need to post some explicit references to what you are talking about
for continued discussion here to be fruitful.
> is a set of
> identical mirror images of a galaxy
If I understood you correctly, this is simply not true.
> that seems to me to indicate a
> preferred direction of propagation along some axis of some type (a
> polarization or something like that?).
There are no polarisation effects in gravitational lensing....
> Is it possible that some sort of
> preferred direction or orientation of electromagnetic propagation is
> responsible for the types of images observed to bend around gravity
> lenses?
Trust me that the basics of gravitational lensing is very well
understood and completely explained by GR. No need to resort to some
speculative explanation when the standard one works fine.
Gordon D. Pusch
> That's what I thought, too. And that may be correct. But then if the
> lens was off-center with the line between me and the galaxy, I'd expect
> to see a distortion in the images of the galaxy, one side being smaller
> and less distorted than the other. But what is observed is a set of
> identical mirror images of a galaxy that seems to me to indicate a
> preferred direction of propagation along some axis of some type (a
> polarization or something like that?). Is it possible that some sort of
> preferred direction or orientation of electromagnetic propagation is
> responsible for the types of images observed to bend around gravity
> lenses?
More likely the effect you are interpreting as implying a ``prefered
direction'' is due to the ``gravity lens'' having some ``cylindrical
aberration'' to it. Most galactic mass-distributions are known to be
_ellipsoidal_, rather than spherically symmetrical as you are tacitly
assuming, which breaks the rotational symmetry of the lensing effect.
-- Gordon D. Pusch
perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;'
Jeff Baldwin
>In article <3A233EB1...@idt.net>, Jeff Baldwin <mv...@idt.net>
>writes:
>
>> Jeff Baldwin <mv...@idt.net> wrote:
>> But what is observed
>
>You need to post some explicit references to what you are talking about
>for continued discussion here to be fruitful.
The photos I saw (in SCIENCE magazine, or something like that) are 10
years or more in the past. But thanks to Chris, I find a more broad
range of images. I'd no idea there was such a plethora of possible lens
effects. I don't see exactly the type of image I had in mind, however.
But, here are some illustrative examples that will suffice:
http://apod.gsfc.nasa.gov/apod/ap990601.html (top row, middle and second
row, right)
http://wfpc2.jpl.nasa.gov/~idt/images/lens.html
http://vela.astro.ulg.ac.be/themes/extragal/gravlens/bibdat/engl/glc_homepage.html
(second row, middle and sixth row, middle)
http://oposite.stsci.edu/pubinfo/PR/95/43.html
http://apod.gsfc.nasa.gov/apod/ap980330.html
>....
>Trust me that the basics of gravitational lensing is very well
>understood and completely explained by GR....
Then I've found the right place for certain. So please tell me (or help
me connect with some resources which I may peruse), what are the causes
of the split images (e.g., top-row-middle of the ap990601.html page) and
the crosses? I "understand" the rings and images like sixth-row-middle
of the vela site, but not the others. Thanks so much.
-Jeff Baldwin
Jonathan Thornburg
Phillip Helbig <hel...@astro.rug.nl> wrote:
>Trust me that the basics of gravitational lensing is very well
>understood and completely explained by GR. No need to resort to some
>speculative explanation when the standard one works fine.
A small addendum (I'm sure Phillip knows this, but some readers may not):
It's interesting to consider what aspects of gravitation enter into
astronomical gravitational lensing. It turns out that it's essential
to consider the bending of *spacetime*, not just of space (otherwise
you loose a factor of 2 in the bending angle). But the gravitational
fields involved are weak enough that (to a degree of approximation
*far* better than the astrophysical uncertainties) we can take the
gravitational field to be *scalar*, i.e. we can fully characterize
it by (the spacetime variation of) a Newtonian gravitational potential
$U$. And we can (again to a very good degree of approximation) linearize
the Einstein equations about flat spacetime, with (if I recall correctly)
only the metric component (in suitable coordinates) $g_{tt} = 1 - 2U$
being important.
--
-- Jonathan Thornburg <jth...@thp.univie.ac.at>
http://www.thp.univie.ac.at/~jthorn/home.html
Universitaet Wien (Vienna, Austria) / Institut fuer Theoretische Physik
"IRAS galaxies are all chocolate chip flavored rather than vanilla
flavored as heretofore supposed. This no doubt accounts for their
diversity and appeal." -- Vader and Simon, Astronomical Journal 94, 865
Phillip Helbig
writes:
> I'd no idea there was such a plethora of possible lens
> effects. I don't see exactly the type of image I had in mind, however.
> But, here are some illustrative examples that will suffice:
>
> http://apod.gsfc.nasa.gov/apod/ap990601.html (top row, middle and second
> row, right)
> http://wfpc2.jpl.nasa.gov/~idt/images/lens.html
> http://vela.astro.ulg.ac.be/themes/extragal/gravlens/bibdat/engl/glc_homepage.html
> (second row, middle and sixth row, middle)
> http://oposite.stsci.edu/pubinfo/PR/95/43.html
> http://apod.gsfc.nasa.gov/apod/ap980330.html
> >....
> >Trust me that the basics of gravitational lensing is very well
> >understood and completely explained by GR....
> Then I've found the right place for certain. So please tell me (or help
> me connect with some resources which I may peruse), what are the causes
> of the split images (e.g., top-row-middle of the ap990601.html page) and
> the crosses?
By "crosses", I guess you mean four-image systems. It is difficult to
point to something and say it is the "cause". So this is deliberately
vague: If the lens itself is symmetrical, then essentially the three
points observer, lens and source determine a plane, and due to symmetry
considerations one gets 2 images. If the lens itself is asymmetrical,
either because it has a quadrupole moment (e.g. is elliptical instead of
spherical) or because of an external perturbation by, say, a nearby
galaxy group ("external shear")---the effects are the same to first
order---then the generic case is four images.
> I "understand" the rings and images like sixth-row-middle
> of the vela site, but not the others. Thanks so much.
Have a look at
http://vela.astro.ulg.ac.be/themes/extragal/gravlens/bibdat/engl/DE/didac3.html
A nice mixture of equations and, err, analog models.
It is really illuminating to get one of these lenses and play around
with it, "getting a feel" for the basic principles, so to speak. As
Chris mentioned, there are also similar things on the web.
Phillip Helbig
writes:
> If a gravitational lens is isotropic, then the image of a galaxy bent
> around such a lens will appear as a symmetric ring instead of bent,
> mirrored images on opposite sides of the lens. But the pictures of such
> lenses that I have seen invariably show the bent, mirrored type of
> "reflection" images and not what I would expect from an isotropic,
> symmetric lens. This seems to me to exhibit a type of broken symmetry.
>
> What am I missing?
>
> Thanks! -Jeff Baldwin
>
> [Moderator's note: you'd have to be awfully lucky for the
> gravitational lens to perfectly lined up between you and
> the galaxy. - jb]
John's explanation is essentially correct. (Actually, in practice one
doesn't have to be so lucky, because some sources are extended, rather
than being point sources, so an approximate alignment will result in an
"Einstein Ring".) One needs to consider not only the symmetry of the
lens, but also whether the alignment is near-perfect enough or not.
Actually, deviation of the lens from radial symmetry (say, elliptical
instead of spherical) also determines things like the number of images
one sees and not just the relative positions (which is more an effect
of the alignment or lack thereof).