.and it is distributed throughout the galactic
halo. This dark matter is occupying the region
that we call galactic halo and extends beyond
the diameter of the galaxy.
When you do the calculation in order to explain
the observed rotation curves, how the rotational
velocity depends on the distance from the
galactic center, it turns out that we must
have five times more dark matter than luminous
mass. In fact, the notion of dark matter was
introduced much earlier, way before mid '70s
by American astronomer of Swiss origin, by
the name of Fritz Zwicky.
He basically came to the idea that there has
to be some matter that does not produce the
light by observing how the galaxies in a cluster
of galaxies called Coma Cluster move. It's
a cluster of galaxies, these blotches that
you can see here, they are individual galaxies
in the cluster, and they are basically gravitationally
bound to each other.
I'll just sketch a few of those galaxies with
their spiral arms. They attract each other
with the force of gravity, they tug on each
other with the force of gravitational attraction,
as a result, they orbit some common center
of mass.
They revolve around the center of mass of
the cluster, just like two stars bound by
the force of gravitational attraction or say
a star in a black hole revolve around the
common center of mass. The galaxies in a galaxy
cluster are bound together by this force of
gravitational attraction, and they revolve
around the center of mass for the entire assembly.
He noticed that they move too fast. If all
of the mass in the cluster was contained only
their stars, the luminous mass. He calculated
by measuring the orbital speed. Again, everything
is based on the third Kaplan's Law formulated
by Newton. He made a calculation how much
mass there has to be for them to be moving
as he observed.
He concluded that the luminous mass was only
1,400 of the total mass that had to be there.
Therefore, he made a conclusion that there
was as he called in German, his native language,
"Dunkle Materie," which is German for dark
matter.
The term dark matter was actually first introduced
by Zwicky. It was all based on his observations
of how fast the galaxies move in the comet
cluster, way before the rotation curves of
the galaxies were measured.
He was an extremely inventive person. He came
up with so many things. For instance, he was
the one to think that they actually in the
transition of the star to the neutron star,
there has to be an event like supernova. That
was proposed by him and another astronomer.
He was a very demanding person, and did not
accept any kind of nonsense.
Therefore, he wasn't getting along with his
colleagues at CalTech, California Institute
of Technology. He used to call them "spherical
bastards." When asked, "Why do you call them
spherical bastards?" he says, "Because they
look like bastards regardless of which direction
you look at them." Spheric has a property
that looks the same regardless of your vantage
point. That was the reason why he called his
colleagues spherical bastards.
Nevertheless, he was extremely inventive,
and [inaudible 05:32] mention his name a bit
later.
That stuff is there. The question is, what
is dark matter? There were several proposals.
One that makes sense immediately, they were
called MACHOs. This is an acronym that stands
for Massive Astrophysical Compact Halo Objects.
There is a reason for this name, as you will
find out later.
The proposal was, these are things that do
not produce light, so what could it be? Could
it be black holes? It could be the neutron
stars whose beams of radiations are just not
crossing us, and therefore we cannot detect
them. It could be also old white dwarves,
white dwarves that formed long time ago and
start fading, losing their thermal energy
that was captured there initially.
Then brown dwarves, the star that never could
quite become main sequence stars because they
didn't have enough mass -- for instance, Jupiter-sized
planets. The question is, how can we detect
a MACHO? If it does not produce light, how
can we detect it?
There is a very neat method that is actually
based on Einstein's theory of relativity that
any mass or energy bends space-time. If the
light bends space-time, it will actually curve
around the massive object. Let me just explain
what gravitational microlensing is. This diagram,
schematically, is explaining what gravitational
microlensing is.
If we are viewing a star from an observatory
on Earth, and there is a MACHO, say a black
hole, passing between the star and us, the
mass contained in this object, say a black
hole, will curve the space-time, curve the
space, and the light will travel along the
path of shortest distance in that curved space.
It would appear to us as if the light from
this star is coming from these two directions.
Moreover, the image gets smeared into these
arches. But the thing is that, with objects
that are not of very high mass, the amount
of bending is not very large. If you have
a brown dwarf, say it's a small mass of less
than .05 of the solar mass, the amount of
bending of light is not large. This bending
angle, or the bending angles, is highly exaggerated
in this diagram.
They are typically 100 times smaller than
the resolution of Hubble Space Telescope.
In other words, Hubble Space Telescope cannot
resolve these small angles. What one sees
is, when the light rays come into the telescope,
you now get more light. There is a brightening
of the star when the black hole passes between
the star and us.
Here's the star and say this is the telescope.
This would be the line of sight to the star
and, say, a MACHO is passing between us and
the star at some distance above the line of
sight. Here is MACHO. It's moving with some
speed, v. It has some mass, m. It passes above
the line of sight at some distance, d. When
it's actually closest to this line of sight,
we will receive most of the light from the
star.
These two images would get together. We will
see brightening of the stars.
If I plot the observed brightness of a star,
say, I'm plotting here brightness of the star
as a function of time. Once the MACHO is closest
to the line of sight, I will see increase
in brightness -- when MACHO is at the closest
distance to the line of sight. The width of
the peak 
depends on the speed of the MACHO, how fast
it's moving.
If it's moving very fast, then it will spend
little time here. The peak is going to be
narrow. If it's moving slower, it will take
longer for it to pass near this line of sight.
Therefore, the width of the peak is going
to increase. It also depends on the mass of
the MACHO. The height of the peak, how high
it is, on this distance of closest approach.
The smaller it is, the peak height is going
to be higher.
By doing these measurements, by looking at
these peaks of many stars in nearby galaxies,
you can actually determine the masses of these
objects. You can detect them so on and so
forth. There were several large international
projects devoted to actually doing precisely
that.
The results of these projects are that the
MACHOs can account for only at most 19 percent
of the mass of the dark matter. Clearly, these
massive astrophysical compact halo objects
can't explain truly the origin of the dark
matter.
The second candidate that was actually proposed
before MACHOs and influenced the name MACHO
are WIMPs. This is the acronym that stands
for Weakly Interacting Massive Particles.
The theory behind this is that basically these
particles have mass quite substantial, much
higher than the mass of neutrinos which have
nearly zero mass and that they interact with
other matter in the universe only through
weak nuclear and gravitational force.
They do not interact via electromagnetic forces.
They don't couple to light. They don't produce
any light. The fact that they do exert gravitational
force actually can then explain why the dark
matter speeds up the stars at the edge of
spiral galaxies or makes galaxies in a galaxy
cluster move faster than what you would expect
based on the amount of luminous matter.
Because they interact with ordinary matter
only via weak nuclear force, they are very
hard to detect. It's possible, but it's difficult.
There are several experiments throughout the
world designed to actually detect these WIMP
particles. So far, none has been detected.
In reality, we don't know what dark matter
is.
It turns out that actually we know very little
about the stuff around us. The composition
of the universe only about five percent is
ordinary matter, the stuff we and stars are
made of. 27 percent is the dark matter. Everything
else, nearly 70 percent, 68 percent is something
that was invoked only since late '90s in order
to explain the acceleration and the expansion
of the universe called dark energy.
We don't know not only what dark matter is.
We have no idea what dark energy is. When
you think about it, what we really understand
today out of the universe is only five percent.
There is a lot of stuff that we still need
to discover.
