We will now talk about gravitational lensing, which is a very powerful
technique to find about distribution of mass in the universe, whether it's
visible or not. As you will recall from the general
relativity, it predicts that the presence of the mass, again whether you can see
it, invisible light or not, will distort the paths of the light rays passing by.
Therefore we have a method of learning about mass distribution, regardless of
whether we can see it in any way. this was originally considered,
considered by Chowlson and Einstein, and also Zwicky, but it took until the 1979
to find the first real example. This was measurement of a quasar, which
we have to have 2 images which are just mirages.
They're both the same quasar and after that hundreds if not thousands of lenses
have been found. So, the geometry shown here, if we have a
perfect alignment of the observer, the background source and the lens.
And distributional symmetric, then each azimuth will be equal and, and so the
image of the background object will be now distorted in to a ring, called the
Einstein ring. If we deviate from that symmetry, either
by moving the lens a little bit in the lens plane, or by changing the mass
distribution to be asymmetric, the ring will break up,
and we'll see multiple images of the lens source.
and this is indeed what's seen in a case of multiple image gravitationalized
quasar. So Zwicky already in 1937 predicted that
gravitational lensing should not only be detected, but it can be used to probe
mass distribution in galaxies in the universe, as well as to use clusters or
galaxies as telescopes to magnify more even distant ones and after all, it can
also be used to test the theory of gravity, all of those predictions have
come true. As far as measuring masses using
gravitational lensing, that took until the 1990's, and Hubble Space Telescope,
in order to be able to really do this well.
These are Hubble Space Telescope images of a particular cluster, that serves as a
gravitational lens. All of these blue arches, arcs and
arclets are images of background galaxies that have been lensed by this cluster,
split and distorted, and thus the cluster itself is essentially a gigantic lens in
space that magnifies and distorts their images.
From the distribution and shape of these arcs and arclets, one can reconstruct the
mass distribution in the cluster regardless of where the galaxies are.
So the gravitational bending of light in general of theory is twice what you heard
from the utonian gravity. Most importantly if it's achromatic,
protons in any wavelength are deflected in exactly same way.
And this is unlike say, plans that were made out of box.
This adds to the power of the method because it's been used not just in
invisible light but in radio and also x-rays.
Obviously the effects would be the strongest for the strongest gravitational
field. and the strongest you can get is if you
compress the lens mass into a black hole. Then you get maximum effect right at
Schwarzschild radius, but in reality that doesn't happen.
Most of the physical objects in galixies are clusters are vastly larger than their
Schwarzschild radii, so the effect isn't quite as strong.
Here is a simple schematic geometry shown.
It is fairly obvious there is observer, the lengths and the source in the
background and destortion of the light path shown here that straight lines must
really curve can be respresented as the angle by which, between the direction to
the lens and the lens image. All these angles are small, usually arc
seconds, or even fractions thereof, and so small angle approximations apply.
There is some fairly straightforward geometry, that then, you can derive from
here, and in the end, you have a quadratic equation that describes the
deflection of light rays, in this particular geometrical setting.
We can simplify that expression a little bit, by introducing Acquainted he called
the Einstein radius, it's really an angle, angular radius if you will and
it's given by this formula. Essentially this is the characteristic
radius in projection away from the lens where distortions will be strongest and.
It may not be a perfect circle, depending on the mass distribution, so the, the
line that connects points to satisfy this criterion, regardless of whatever the
mass distribution is, is called critical line.
Generally speaking, for deflections within Einstein radius or thereabouts,
the, you'll see multiple images, that's called strong lens.
for deflections further out you'll see only distortions but generally not
multi-split images, that's called the weak lensing regime.
So quadratic equation is not shown very simply and it has 2 obvious solutions
that, this is high school math. And so, in the cases where a lens isn't
perfectly aligned, there are at least two solutions, corresponds to, to different
images. One inside, and one outside the Einstein
radius. I mentioned different lensing regimes.
If the deflection is strong, hence the image splitting, that is called strong
lensing regime. however, deflections will occur even
further out, and obviously, the further out you go, the weaker the effect.
But, nevertheless, they'll be detectable in the form of image distortion.
And that's called the weak lensing urgings, that turns out to be a very
important for studies of cluster mass distribution.
If you can map all of the distorted images, you can, in principle,
reconstruct the distribution of mass that led to the lensing This has been done on
galaxies as well as cluster with galaxies we're talking about something in the of
the order of an arc second. Observations with Hubel telescopes were
essential to do this. A particular group called SLACS
collaboration is one of them. they studied fairly large sample of
galaxies acting as lenses to some background galaxies that appearing as are
thin lenses or as segments thereof, and with some reasonable assumptions they can
infer the mass distributions in projection for the lensing galaxies.
The results are sh, shown schematically here for a handful of cases.
The lines on the plots describe density distribution as a function of radius, for
visible matter, which is just measured stars, or other massive stars, for, the
whole thing that causes the distortion, and the difference which represents
contribution of the dark matter halo. as you can see, a smaller radii, visible
material dominates, something we already learned from kinematical studies.
As you go further out in radius, the dark matter component becomes inevitable, and
dominates the geometry. We can simulate the effects of
gravitationalizing, by taking an image of the sky, placing fictitious lens of given
mass distribution in front, and seeing what it will do to the picture behind it.
From that, we can then learn how to invert actual observations to derive
distribution of mass That is doing the lensing.
These are simulations so you can see that clearly that the effects are the
strongest in the middle and get weaker and weaker the further out you go.
This is another simulatio used to illustrate this.
Imagine that somehow there is a gigantic graph paper in the sky.
and then you put a cluster of galaxies in front of it, then it will distort the
geometry of the background as shown here. It is complicated because it's not a
simple, simple mass distribution. There are many different galaxies.
Each of them acts like little lensing, in, you know, of itself, and together
they have a collective effect. So inverting these geometries can be a
very complicated business. Nevertheless, the metal is well
understood now and a lot of good data have been obtained.
Many clusters have been studied using this technique.
Here is an example of a particular cluster, where different contours show,
say, average distribution of galaxy light,
or the number density, or the inferred galaxy mass, or mass distribution for the
whole cluster. This was done for quite a number of
clusters. A small subset is shown here,
and lensing gives a new independent estimate of the lensing mass in a
cluster, regardless of whether it's baryons, or dark baryons, or dark matter
or anything. As long as it's some matter of any kind
that exerts gravitational pull, it will contribute.
And remarkably enough, the inferred mass to light ratios for clusters, are in
excellent agreement with those we inferred from using very old theorem
arguments, from either X-ray gas or Galaxy velocity dispersion.
This is completely different physics and different kind of measurement,
and this is why we believe, that indeed, there is some kind of dark mass there.
We see its effects not just in kinematics of test particles like galaxies or
protons or electrons but also in manifestations of general activity.
The geometry of the images seen as the lensing mass.
For this reason, people really believe that we are, indeed, dealing with dark
matter, and it's not something like the
distortion of gravity, because that will spoil gravitational
lensing, and you never get the same result as you
would for measurements using variable care.
This is one thing, for example, that Monde cannot possibly reproduce.
This kind of study is, is now done not just for big clusters of galaxies, but
just in general deep field surveys, where we measure a lot of faint galaxies, and
sometimes get measurements of their redshifts.
The, what's shown here is a snapshot from one such survey called COSMOS, and what's
show on the left is the smoother distribution of light that's observing
galaxies. What's shown on the right is the
reconstructed distribution of mass in projection that is determined from the
distortions of the images of galaxies in the background.
Because, they measured distance's to galaxies, then they can actually
constructed 3-dimensional dark matter in space, and the resolution isn't very good
still, but here it is. It's actually remarkable that we can map
mass distribution in space, because the physiological distances in full
3-dimension's, even though we don't see the mass.
This is likely to become a very powerful tool in our underst, our understanding of
structure formation. Next we will talk about Gravitational
Microlensing. That's lensing of stars by stars and it
was used to constrain contributions of matches to the dark mass.