If galaxies are fun. Let's move one scale 
up in the hierarchy to clusters of 
galaxies and let's see what we know about 
them. 
so, our galaxy, like most galaxies, is 
part of a cluster or Local Group, as we 
call our clusters, quite small, 
is dominated by the three giant spirals, 
the Milky Way, slightly larger M31 and 
M33 in Triangulum, the Triangulum galaxy, 
and the estimated mass of this entire 
collection of galaxies is 4 * 10^2 solar 
masses, of which, at most 10% is 
barionic, which is the name we give to 
normal matter, 
stuff where the mass is mostly protons. 
And so, most of the mass of this cluster 
is dark matter and we get that by 
estimating the masses of the galaxies 
based on star counts and gas counts and 
our understanding of galaxies. 
And, comparing that to the kinematics, 
the Newtonian calculation of the total 
mass that all of this is orbiting. And 
based on the motion a merger of the Milky 
Way with Andromeda in about 4 billion 
years is a distinct possibility. 
Of course, that won't be of too much 
interest to denizens of the solar system, 
because in 4 billion years, life here 
will have changed due to stellar 
evolution, 
but it will be a very interesting 
experience for anybody still living on 
some planet in the Milky Way. 
Note that it's not as remember, a 
galactic collision is a stately affair. 
galaxies are mostly empty space, 
stars only interact gravitationally. 
if these were objects full of gas, there 
would be a lot of friction and some 
establishment of a combined angular 
momentum and a combined disc. 
In this case the merger of these two 
ellipticals may two, these two spirals 
may well end up as a elliptical galaxy, 
because there's not enough friction to 
settle everything down into into a disk. 
this is are local clusters, a very small 
cluster, a far more sizable cluster is 
the well-known Virgo cluster in the 
constellation, you guessed it 
that has 250 large galaxies and about 
2,000 smaller ones scattered over a 
distance of 16 million parsecs. And of 
these galaxies, 68% are spirals and only 
about 20% are ellipticals, but that 
includes four huge, giant ellipticals 
with a radius of between 1-300 
kiloparsecs. 
So three or eight times bigger than the 
solar system or 12 times bigger than the 
Milky Way I mean. 
and this includes the center of the 
cluster is dominated by three out of 
these four ellipticals, as we said, 
ellipticals are often found at the 
centers of dense clusters. 
And 
the galactic clusters, as I said, are 
different from star clusters, in that, 
the intercluster medium of hot gas 
contains on average about 8 times more 
mass than the sum total of all the mass 
of all the galaxies. 
about 10% of the mass, by the way is 
accounted for by intergalactic stars, 
which were suspected that only recently 
directly. This involves detecting 
individual stars in a cluster so these 
clusters are somewhat distant and 
recently that success has been achieved. 
here is a beautiful image to the right, 
an optical image of a cluster Abell 2199. 
You see the individual galaxies shining 
when you look at the x-ray image, you see 
that the entire cluster is glowing in 
x-rays because there is a large density 
of hot gas, and most of the mass, most of 
the baryonic mass of a cluster is in the 
form of gas and this is quite important. 
Now as usual, I keep saying baryonic 
mass, because as everywhere else in the 
universe, most of the mass is in the form 
of this mysterious dark matter. 
And 
how do we know? How do we find dark 
matter in a cluster far, far away? Well, 
we can compute the total mass. 
we can also use gravitational lensing by 
clusters to produce the mass distribution 
of the lense. 
Remember, that the gravitiational lensing 
equation that I wrote said that the 
deflection by which light of a angle of a 
beam of light passing a distance or a 
distance of nearest approach r, 
and I think I called it b from an object 
of mass M is given by this. 
You can imagine trying to compute what 
distribution of masses would cause the, 
the lensing image we produce. 
It's some kind of inverse, scattering 
problem. 
We see here a rich cluster along with you 
can see here and there some lensed 
images, 
and superposed this sort of blue smooth, 
blue over coloring is the calculate, 
calculated distribution of dark matter or 
of the total mass of the cluster, the 
lensing mass superposed on the image of 
the galaxies. 
And we see that while the galaxies show 
up at this distance as individual dots of 
light, the mass distribution is very 
smooth. 
The dark matter does not clump nearly as 
much as the galaxies do, and in this 
case, it's very interestingly 
distributed. 
There's a sort of clump of dark matter at 
the core of the cluster and then a ring 
of dark matter surrounding the cluster, 
the dynamics of how this happened are far 
from clear, I should say. 
And here is a map that gives, makes the 
same point. 
This is a three-dimensional plot where 
the two axis are sort of along the plane 
of the image we were just looking at, 
the vertical axis is the mass 
distribution. We see the spikes, those 
are the galaxies, very dense regions of 
mass, but we see that most of the mass is 
contained, this is a different cluster, 
but still, most of the mass is contained 
in the big smooth distribution underlying 
these individual peaks. Most of the mass 
of a cluster is not in the galaxies, 
that would be true even absent in dark 
matter, but most of the mass of the 
cluster is not even in the intracluster 
gas, which is itself eight times the 
galactic masses. 
It's actually in the dark matter content 
which is larger still. 
And, this brings us to one of the most 
pretty observations of 2006 an object 
called the Bullet Cluster. 
And, there is a lot going on in this 
image, so let's pay attention for a 
second. 
what we see here is the process of two 
galactic clusters in the process of 
colliding and essentially merging. 
And the image has three pieces to it, 
there's an optimal image where we see two 
concentrations of galaxies over here on 
the left, one concentration of galaxies, 
and over here on the right, a second 
concentration of galaxies. 
the collision occurred somewhere around 
here. 
How do we see that? Well, the pink is the 
glow of the heated gas, 
the infared light from gas that has been 
heated by the collision, and this is the 
difference between two galaxies colliding 
and two clusters colliding. 
When two galaxies collide they basically 
pass through each other, other than 
gravitational dynamical friction, because 
galaxies are made of stars. 
Clusters are mostly gas, so most of 
gas two clouds of gas that collide, 
actually, interact strongly with each 
other, compress, and heat up. 
So, when these two clusters pass through 
each other, essentially, the galaxies 
went through, but the gas was trapped in 
the middle. 
And so the entire gas content of the two 
galaxies in contain, is contained in 
those two pink shock wavy, glowing 
collections of gas. 
Okay, so the galaxies go through and the 
gas gets stuck. 
Where does the mass go? Here is the 
question. So they, luckily behind these 
colliding clusters are background 
galaxies whose lensing images we can 
study. 
And we can use that, just as we did in 
the previous picture to draw a mass 
distribution for this object. And, based 
on everything I said, the mass 
distribution, since the gas in a cluster 
is eight times more massive than the 
galaxies, you'd expect the mass 
distribution to be centered in the middle 
where the gas is, if it was a gas. What 
we see in blue is the mass distribution, 
and we see that the mass distribution, 
like the galaxies, basically went right 
through. 
Most of the mass of the cluster is not in 
the gas, it's in the even more massive 
dark matter halo of the cluster, 
and dark matter being weakly interacting, 
sailed right through. 
So in some sense, the fact that dark 
matter follows the galaxies is 
paradoxically the, the fact that the mass 
follows the galaxy is a validation of the 
fact that the mass is not in the forms of 
matter we're familiar with. 
In terms of those, most of the masses in 
the dust, 
we see the dust right there in the 
middle, we see the galaxies and the dark 
matter following through, and this is a 
very pretty image. 
some have called it a direct detection of 
dark matter, and this is a not consistent 
with most modified Newtonian dynamic 
theories, which suggested modifying 
gravity. 
So this clusters it. The universe is made 
up of galaxies which fit into clusters. 
Well, no, there is, follow Kant, there is 
a hierarchy, hierarchy of structures 
clusters are organized in superclusters, 
indeed, our local group is on the edges 
of the local superclusters. 
Supercluster of which Virgo is at 16 
megaparsecs away from us, is the center, 
the size of the cluster is about 20 
megaparsecs. 
at larger distances, we find more 
superclusters and we can look at try to 
understand the local motions relative to 
the Hubble flow. 
over and above the sort of expanding 
Hubble flow. 
And motions of galaxy clusters in the 
local neighborhood that we live in, 
suggests a great attractor in Centaurus, 
some object with a mass of 10^16, I 
believe, solar masses. 
There is nothing in that region that has 
sufficient mass, unless it's mostly dark 
matter in ways we're not familiar. 
The Shapley Supercluster over here is the 
most likely candidate for housing that 
great attractor, but it's not been 
observed. 
and so, this is a map of all of the 
superclusters this is a map of I think a 
100 million or a 100 megaparsec around 
the the Milky Way, and we see the con, 
the, the, the local region strewed with 
super clusters of galaxies. 
And now when asked, are superclusters 
clustered into superduper clusters, at 
what level does this stop? And that's a 
very important question. 
The question is, is there a structure at 
all scales? Is the universe lumpy all the 
way up to forever? At any size, there are 
a super-duper-hyper clusters. 
And, to try to answer this at the largest 
scales there is a famous survey that was 
done which found I believe hundreds of 
thousands or couple hundreds of thousands 
of galaxies. 
and, this was an attempt to look deep 
into the sky and in order to avoid 
interference from the Milky Way the 
survey picked out two sort of slices of 
the sky that avoid interference from the 
galactic plane and are, or oriented at 
gaps in the galactic discs, so that we 
can see far away without galactic 
interference. 
And they map out to z of 0.23, you can 
compute the distance. And, the structure 
of these two sheets as found by this 
galaxy redshift survey is here, the, sort 
of two slices are 
these are two narrow angular slices that 
they surveyed. 
And as a function of distance and angle 
within the slice, we see here the 
structure of all the galaxies they found. 
And you see here redshift, on the one 
hand, and distance in billions of light 
years, this was quite a deep sky survey 
and we see lumpiness. 
We see these structures, these sort of 
filaments. 
Remember this is a slice, so these are 
presumably slices through some 
two-dimensional structures surrounding 
large relatively empty bubbles or so 
called voids. And sort of 
three-dimensionalish representation of 
the way space looks in our vicinity is 
over on the right. And, again you see 
that there are these large gaps where 
very, almost nothing is, so there is 
structure at these very large scales. 
so is there, does, is the suggestion here 
that there is structure at all levels? 
Well, not quite. 
You measure structure mathematically by 
something called correlation, this 
roughly tells you the answer to the 
question, if I find a galaxy or a cluster 
here how does this change the probability 
of finding another cluster at some 
distance from there and at small 
distances? Yeah, 
if we find a galaxy here, then, since all 
galaxies are members of clusters, there 
is very likely to be one very close to 
it. and this is a plot of the sort of 
correlation coefficient as a function 
logarithmically of distance. 
And we see that correlations decline, and 
the prediction is, from this graph, that 
a distance is well above 100 megaparsec, 
correlations disappear. 
Correlations disappear, means that if you 
find a collection of galaxies here at a 
distance of 100 megaparsecs, it tells you 
nothing about the probably of finding 
more galaxies, so the universe at 
distances of say a billion parsec should 
be quite smoother of 500 megaparsecs, 
exactly where you'd draw the line is 
clear, is not clear, but at large 
distances, the universe is homogeneous. 
You, all of the perturbations smooth out 
at very large distances, 
there is not an infinite hierarchy of 
super-duper-duper clusters, 
at large distances, we see homogeneity. 
Now, even so, the size of these voids is 
interesting. 
these are large regions of a galaxy of 
the universe where there are very few 
galaxies. 
How did they form? Well, we don't yet 
know. 
There are various theories of early 
universe structure formation. We might 
talk about them next week, but what is 
important is all of these voids have to 
be primordial. 
We are looking at the way the universe 
look essentially at its creation, because 
in the 13 billion years since the Big 
Bang, there has not been time for 
galaxies, that might have populated, or 
matter that might have populated these 
voids to have moved out, 
these voids are just too large. 
Now, this statement, that the universe is 
homogeneous at scales above 100 
megaparsecs or well above a 100 
megaparsecs is something we will use 
heavily in understanding cosmological 
considerations next week and is used 
successfully by cosmologists, but nothing 
is an axiom. 
recently, there's been reports of a 
collection of quasars of essentially 
active galactic nuclei which are 
scattered in what appears to be a 
coherent structure that is more than a 
billion parsecs across. 
So these black dots are this sheet of 
what seems to be correlated structure, 
some kind of coherent structure that is a 
billion parsecs across. 
That is beginning to stretch the limits 
of our understanding of structure 
formation. 
This is a brand new result. 
We'll see how it either stands up to 
validation, 
and if so, how it gets incorporated into 
models of structure formation. 
As always in this class, science is a 
seem, succession of approximations to a 
truth. This might be the beginning of an 
improvement in our understanding, or it 
might just be a blip.