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If galaxies are fun. Let's move one scale 
up in the hierarchy to clusters of 

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galaxies and let's see what we know about 
them. 

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so, our galaxy, like most galaxies, is 
part of a cluster or Local Group, as we 

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call our clusters, quite small, 
is dominated by the three giant spirals, 

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the Milky Way, slightly larger M31 and 
M33 in Triangulum, the Triangulum galaxy, 

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and the estimated mass of this entire 
collection of galaxies is 4 * 10^2 solar 

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masses, of which, at most 10% is 
barionic, which is the name we give to 

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normal matter, 
stuff where the mass is mostly protons. 

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And so, most of the mass of this cluster 
is dark matter and we get that by 

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estimating the masses of the galaxies 
based on star counts and gas counts and 

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our understanding of galaxies. 
And, comparing that to the kinematics, 

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the Newtonian calculation of the total 
mass that all of this is orbiting. And 

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based on the motion a merger of the Milky 
Way with Andromeda in about 4 billion 

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years is a distinct possibility. 
Of course, that won't be of too much 

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interest to denizens of the solar system, 
because in 4 billion years, life here 

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will have changed due to stellar 
evolution, 

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but it will be a very interesting 
experience for anybody still living on 

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some planet in the Milky Way. 
Note that it's not as remember, a 

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galactic collision is a stately affair. 
galaxies are mostly empty space, 

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stars only interact gravitationally. 
if these were objects full of gas, there 

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would be a lot of friction and some 
establishment of a combined angular 

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momentum and a combined disc. 
In this case the merger of these two 

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ellipticals may two, these two spirals 
may well end up as a elliptical galaxy, 

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because there's not enough friction to 
settle everything down into into a disk. 

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this is are local clusters, a very small 
cluster, a far more sizable cluster is 

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the well-known Virgo cluster in the 
constellation, you guessed it 

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that has 250 large galaxies and about 
2,000 smaller ones scattered over a 

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distance of 16 million parsecs. And of 
these galaxies, 68% are spirals and only 

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about 20% are ellipticals, but that 
includes four huge, giant ellipticals 

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with a radius of between 1-300 
kiloparsecs. 

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So three or eight times bigger than the 
solar system or 12 times bigger than the 

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Milky Way I mean. 
and this includes the center of the 

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cluster is dominated by three out of 
these four ellipticals, as we said, 

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ellipticals are often found at the 
centers of dense clusters. 

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And 
the galactic clusters, as I said, are 

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different from star clusters, in that, 
the intercluster medium of hot gas 

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contains on average about 8 times more 
mass than the sum total of all the mass 

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of all the galaxies. 
about 10% of the mass, by the way is 

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accounted for by intergalactic stars, 
which were suspected that only recently 

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directly. This involves detecting 
individual stars in a cluster so these 

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clusters are somewhat distant and 
recently that success has been achieved. 

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here is a beautiful image to the right, 
an optical image of a cluster Abell 2199. 

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You see the individual galaxies shining 
when you look at the x-ray image, you see 

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that the entire cluster is glowing in 
x-rays because there is a large density 

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of hot gas, and most of the mass, most of 
the baryonic mass of a cluster is in the 

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form of gas and this is quite important. 
Now as usual, I keep saying baryonic 

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mass, because as everywhere else in the 
universe, most of the mass is in the form 

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of this mysterious dark matter. 
And 

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how do we know? How do we find dark 
matter in a cluster far, far away? Well, 

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we can compute the total mass. 
we can also use gravitational lensing by 

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clusters to produce the mass distribution 
of the lense. 

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Remember, that the gravitiational lensing 
equation that I wrote said that the 

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deflection by which light of a angle of a 
beam of light passing a distance or a 

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distance of nearest approach r, 
and I think I called it b from an object 

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of mass M is given by this. 
You can imagine trying to compute what 

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distribution of masses would cause the, 
the lensing image we produce. 

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It's some kind of inverse, scattering 
problem. 

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We see here a rich cluster along with you 
can see here and there some lensed 

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images, 
and superposed this sort of blue smooth, 

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blue over coloring is the calculate, 
calculated distribution of dark matter or 

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of the total mass of the cluster, the 
lensing mass superposed on the image of 

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the galaxies. 
And we see that while the galaxies show 

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up at this distance as individual dots of 
light, the mass distribution is very 

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smooth. 
The dark matter does not clump nearly as 

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much as the galaxies do, and in this 
case, it's very interestingly 

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distributed. 
There's a sort of clump of dark matter at 

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the core of the cluster and then a ring 
of dark matter surrounding the cluster, 

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the dynamics of how this happened are far 
from clear, I should say. 

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And here is a map that gives, makes the 
same point. 

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This is a three-dimensional plot where 
the two axis are sort of along the plane 

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of the image we were just looking at, 
the vertical axis is the mass 

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distribution. We see the spikes, those 
are the galaxies, very dense regions of 

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mass, but we see that most of the mass is 
contained, this is a different cluster, 

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but still, most of the mass is contained 
in the big smooth distribution underlying 

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these individual peaks. Most of the mass 
of a cluster is not in the galaxies, 

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that would be true even absent in dark 
matter, but most of the mass of the 

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cluster is not even in the intracluster 
gas, which is itself eight times the 

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galactic masses. 
It's actually in the dark matter content 

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which is larger still. 
And, this brings us to one of the most 

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pretty observations of 2006 an object 
called the Bullet Cluster. 

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And, there is a lot going on in this 
image, so let's pay attention for a 

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second. 
what we see here is the process of two 

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galactic clusters in the process of 
colliding and essentially merging. 

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And the image has three pieces to it, 
there's an optimal image where we see two 

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concentrations of galaxies over here on 
the left, one concentration of galaxies, 

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and over here on the right, a second 
concentration of galaxies. 

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the collision occurred somewhere around 
here. 

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How do we see that? Well, the pink is the 
glow of the heated gas, 

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the infared light from gas that has been 
heated by the collision, and this is the 

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difference between two galaxies colliding 
and two clusters colliding. 

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When two galaxies collide they basically 
pass through each other, other than 

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gravitational dynamical friction, because 
galaxies are made of stars. 

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Clusters are mostly gas, so most of 
gas two clouds of gas that collide, 

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actually, interact strongly with each 
other, compress, and heat up. 

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So, when these two clusters pass through 
each other, essentially, the galaxies 

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went through, but the gas was trapped in 
the middle. 

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And so the entire gas content of the two 
galaxies in contain, is contained in 

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those two pink shock wavy, glowing 
collections of gas. 

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Okay, so the galaxies go through and the 
gas gets stuck. 

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Where does the mass go? Here is the 
question. So they, luckily behind these 

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colliding clusters are background 
galaxies whose lensing images we can 

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study. 
And we can use that, just as we did in 

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the previous picture to draw a mass 
distribution for this object. And, based 

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on everything I said, the mass 
distribution, since the gas in a cluster 

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is eight times more massive than the 
galaxies, you'd expect the mass 

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distribution to be centered in the middle 
where the gas is, if it was a gas. What 

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we see in blue is the mass distribution, 
and we see that the mass distribution, 

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like the galaxies, basically went right 
through. 

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Most of the mass of the cluster is not in 
the gas, it's in the even more massive 

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dark matter halo of the cluster, 
and dark matter being weakly interacting, 

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sailed right through. 
So in some sense, the fact that dark 

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matter follows the galaxies is 
paradoxically the, the fact that the mass 

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follows the galaxy is a validation of the 
fact that the mass is not in the forms of 

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matter we're familiar with. 
In terms of those, most of the masses in 

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the dust, 
we see the dust right there in the 

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middle, we see the galaxies and the dark 
matter following through, and this is a 

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very pretty image. 
some have called it a direct detection of 

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dark matter, and this is a not consistent 
with most modified Newtonian dynamic 

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theories, which suggested modifying 
gravity. 

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So this clusters it. The universe is made 
up of galaxies which fit into clusters. 

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Well, no, there is, follow Kant, there is 
a hierarchy, hierarchy of structures 

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clusters are organized in superclusters, 
indeed, our local group is on the edges 

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of the local superclusters. 
Supercluster of which Virgo is at 16 

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megaparsecs away from us, is the center, 
the size of the cluster is about 20 

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megaparsecs. 
at larger distances, we find more 

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superclusters and we can look at try to 
understand the local motions relative to 

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the Hubble flow. 
over and above the sort of expanding 

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Hubble flow. 
And motions of galaxy clusters in the 

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local neighborhood that we live in, 
suggests a great attractor in Centaurus, 

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some object with a mass of 10^16, I 
believe, solar masses. 

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There is nothing in that region that has 
sufficient mass, unless it's mostly dark 

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matter in ways we're not familiar. 
The Shapley Supercluster over here is the 

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most likely candidate for housing that 
great attractor, but it's not been 

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observed. 
and so, this is a map of all of the 

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superclusters this is a map of I think a 
100 million or a 100 megaparsec around 

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the the Milky Way, and we see the con, 
the, the, the local region strewed with 

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super clusters of galaxies. 
And now when asked, are superclusters 

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clustered into superduper clusters, at 
what level does this stop? And that's a 

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very important question. 
The question is, is there a structure at 

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all scales? Is the universe lumpy all the 
way up to forever? At any size, there are 

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a super-duper-hyper clusters. 
And, to try to answer this at the largest 

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scales there is a famous survey that was 
done which found I believe hundreds of 

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thousands or couple hundreds of thousands 
of galaxies. 

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and, this was an attempt to look deep 
into the sky and in order to avoid 

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interference from the Milky Way the 
survey picked out two sort of slices of 

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the sky that avoid interference from the 
galactic plane and are, or oriented at 

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gaps in the galactic discs, so that we 
can see far away without galactic 

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interference. 
And they map out to z of 0.23, you can 

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compute the distance. And, the structure 
of these two sheets as found by this 

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galaxy redshift survey is here, the, sort 
of two slices are 

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these are two narrow angular slices that 
they surveyed. 

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And as a function of distance and angle 
within the slice, we see here the 

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structure of all the galaxies they found. 
And you see here redshift, on the one 

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hand, and distance in billions of light 
years, this was quite a deep sky survey 

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and we see lumpiness. 
We see these structures, these sort of 

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filaments. 
Remember this is a slice, so these are 

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presumably slices through some 
two-dimensional structures surrounding 

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large relatively empty bubbles or so 
called voids. And sort of 

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three-dimensionalish representation of 
the way space looks in our vicinity is 

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over on the right. And, again you see 
that there are these large gaps where 

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very, almost nothing is, so there is 
structure at these very large scales. 

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so is there, does, is the suggestion here 
that there is structure at all levels? 

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Well, not quite. 
You measure structure mathematically by 

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something called correlation, this 
roughly tells you the answer to the 

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question, if I find a galaxy or a cluster 
here how does this change the probability 

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of finding another cluster at some 
distance from there and at small 

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distances? Yeah, 
if we find a galaxy here, then, since all 

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galaxies are members of clusters, there 
is very likely to be one very close to 

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it. and this is a plot of the sort of 
correlation coefficient as a function 

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logarithmically of distance. 
And we see that correlations decline, and 

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the prediction is, from this graph, that 
a distance is well above 100 megaparsec, 

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correlations disappear. 
Correlations disappear, means that if you 

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find a collection of galaxies here at a 
distance of 100 megaparsecs, it tells you 

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nothing about the probably of finding 
more galaxies, so the universe at 

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distances of say a billion parsec should 
be quite smoother of 500 megaparsecs, 

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exactly where you'd draw the line is 
clear, is not clear, but at large 

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distances, the universe is homogeneous. 
You, all of the perturbations smooth out 

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at very large distances, 
there is not an infinite hierarchy of 

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super-duper-duper clusters, 
at large distances, we see homogeneity. 

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Now, even so, the size of these voids is 
interesting. 

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these are large regions of a galaxy of 
the universe where there are very few 

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galaxies. 
How did they form? Well, we don't yet 

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know. 
There are various theories of early 

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universe structure formation. We might 
talk about them next week, but what is 

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important is all of these voids have to 
be primordial. 

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We are looking at the way the universe 
look essentially at its creation, because 

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in the 13 billion years since the Big 
Bang, there has not been time for 

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galaxies, that might have populated, or 
matter that might have populated these 

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voids to have moved out, 
these voids are just too large. 

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Now, this statement, that the universe is 
homogeneous at scales above 100 

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megaparsecs or well above a 100 
megaparsecs is something we will use 

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heavily in understanding cosmological 
considerations next week and is used 

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successfully by cosmologists, but nothing 
is an axiom. 

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recently, there's been reports of a 
collection of quasars of essentially 

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active galactic nuclei which are 
scattered in what appears to be a 

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coherent structure that is more than a 
billion parsecs across. 

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So these black dots are this sheet of 
what seems to be correlated structure, 

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some kind of coherent structure that is a 
billion parsecs across. 

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That is beginning to stretch the limits 
of our understanding of structure 

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formation. 
This is a brand new result. 

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We'll see how it either stands up to 
validation, 

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and if so, how it gets incorporated into 
models of structure formation. 

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As always in this class, science is a 
seem, succession of approximations to a 

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truth. This might be the beginning of an 
improvement in our understanding, or it 

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might just be a blip.