So far we have discussed large scale structure in a sense of where the galaxies
are. But where are they moving?
So let's find out what we mean by the term of peculiar velocity for galaxies is a
velocity component in addition to their Hubble flow, due to the expansion of the
universe. So in other words If the galaxy was at
rest compared to, say, microwave background in comoving coordinates, it
will have peculiar velocity of 0. The only component we could observe for it
would be due to the radial expansion of the universe.
Now even though velocities are three-dimensional vectors, we can only
observe the radial component. Due to the velocity because galaxies move
way too slow to, on the sky to actually be able to measure them.
So if you're interested in some aspect of cosmological expansion then these peculiar
velocities are like velocity noise atop of the actual Hubble hole signal.
And so for example, if you're plotting a Hubble diagram which is some form of
distance versus [unknown] you can have errors in distances but you can also have,
well it's not really an error in velocity, but a shift.
In other words it's error in a sense if you assume that velocity is All made due
to the expansion of the universe. And the origin of this is obvious.
If there is a large-scale density field, there has to be a large-scale peculiar
velocity field. A reason for this is that during the age
of the universe, galaxies will fall towards the nearest massive structures to
them. Acquire velocity gradually from zero to
whatever they have today. So in some sense, the pattern of peculiar
velocities has to reflect a pattern of the density distribution.
Now there is one peculiar velocity, some people say only one, which we know with a
great deal of precision. And this is our motion, relative to the
cosmic microwave background. This causes a dipole cosmic micro
background is a little hotter in the direction that we're moving to, and the
velocity is about 620 kilometers per second in a particular direction in the
sky. It turns out this is fairly [unknown] with
typical peculiar velocities in the large scale structure around us today, or for
galaxies maybe a little less - couple hundred kilometers per second.
But Virgo cluster has Hubble Recession velocity of only like 1000 or 1200
kilometres per second. So a peculiar velocity component like this
could really make a difference. So we have a simple equation that relates
total observed velocity. The distance to the galaxy, Hubble
constant and it's peculiar velocity. So we can easily measure a total velocity
that's the redshift. We can ostensibly measure Hubble constant.
But then the tricky part is the distances. So the errors in stimation of distances to
galaxies will map directly into the errors in estimates of their peculiar velocities.
You may recall that there is a number of distance indicators for galaxies which we
can use to compute their distances. They're not given by the redshift.
But each one of them has its intrinsic scatter.
And each one of them will then yield errors in the estimates of the peculiar
velocity. For most part peculiar velocities are
comensurate with Hubble velocities, only in the nearest universe.
And, if we go further say, beyond local supercluster, most of the velocities due
to Hubble expansion. But the fractional error of the Hubble
expansion times the velocity gives you the absolute error of the peculiar velocity
and so the sensitivity is much higher. Sometimes we measure distances not to
individual galaxies but clusters to which they belong and that's were we can hour
its measurement over a large number of galaxies have improved the corresponding
measurement for the entire cluster, so measuring distance to galaxies is very
tricky as we probably recall from the various chapter, but there is another way
in which we can measure peculiar velocities and that is from red shift
surveys themselves. Now, first remember about the redshift
space. We observe some structure of galaxies an
individual galaxy and if it is a very massive structure it's realized like core
of rich a cluster. Galaxies will have their own Thermo
velocity due to the potential well of the cluster itself.
Now we do not measure the component that conventional in the sky, but the radio
component will be there. And so, the higher the velocity dispersion
in the cluster, the more will galaxies scatter in velocity around their true
Hubble expansion value. And if you assume, naively, that measured
velocity is only Hubble velocity in converting to distance, then a spherical
cluster will become allocated along the line of sight, due to these peculiar
components. That is known as the finger of God effect.
On the other hand. If we are still in a linear regime, that
is, low density, contrast, galaxies are slowly falling toward some filament or
sheet, then the opposite will happen, there will be some intrinsic width of that
filament on the skies, it's perpendicular through our line of site.
The galaxies falling towards it, on the side, on our side, will acquire a little
external velocity, will look like, look like they are little further away than
they are. Galaxies on the other side are falling
back. This is what they look like.
They look closer than they really are. The net effect of that is that the
filament looks thinner in the radio direction than it really is.
So statistically, you can do this for whole ensemble galaxies including
[inaudible] survey. And what's shown here is a density plot
that, that corresponds to radial component of the distance, as well as the orthogonal
component. Which you can measure from angular
suppression of the sky. So note that there's two features to this.
A very small angular separations, which will largely be for galaxies that really
are physically close together like in clusters or galaxies.
You see a vertical elongation, the finger of God effect.
But for most of the rest, you see flattening of the distribution which
normally should be spherical. The flattening is due to that linear
infall into the structures along the line of sight.
So, how can we measure peculiar velocities, when all we are measuring is
total velocities in our Redshift survey. It goes like this.
You assume first that galaxies are where they're observed velocities imply.
That gives you first approximation to the density distribution in space.
Then, making some assumptions about mass to light ratios and dark matter and so on.
You figure out how much would galaxies there would have acquired in terms of
peculiar velocities through the history of the universe and then you subtract the
component from the original measured velocity.
You reevaluate the density field at that point and repeat this several times.
At that point you should have, statistically at least, a good separation
between true distribution in space and the peculiar velocity distribution.
So you can do this without measurement or distances altogether.
However, the prob, the problem is that there is a model dependence.
So you have to assume something about, say amounts of dark matter in these structures
and so on. So here is the local kinematics of the
large-scale structure plot. We are falling towards virgo with the
speed of about 270 kilometres per second. The whole local supercluster is moving in
the direction of Hydra-Centaurus supercluster at somewhat higher speed.
And things may acutally go even beyond that.
So here's map of galaxies in the sky. The band in the middle is the galactic
plane, the zone of avoidance, and you can see large structure of many elements
labeled. The hatched blue area on the left
corresponds to replication of the masses. Or mass responsible for our peculiar
velocity which was called the great attractor for a period of time, but I
think now people refer to it by it's original name of the hydra centaurus
supercluster. So I mentioned it, given a peculiar
velocity field, you can derive the underlying density field which must be
responsible for it. And here examples of what it might look
like in projection to the super galactic plane.
Of course, the real thing is in three dimensions.
But here in this density of But here in this landscape, the height corresponds to
the local density, and the plot on the upper right shows the vector field, the
velocities that correspond to those density distribution.
So we're in the middle of this map, in the valley.
A little bump next to us is the local super cluster, and the much bigger
mountain to the left is the Great Detractor.
The large mountain on the other side is Perseus-Pisces Supercluster.
And so if you'll look at the velocity field just above it, you'll see that
there's a [unknown] flow between these two massive structures.
You can do this with any Redshift survey, and it, it was indeed done so.
That's good, because these are tricky measurements, and it's good to do them as
many independent times as possible. You may remember there is, there was a
survey based on IRAS [inaudible] galaxies which is called PSCz Survey, and this is
what their density distributional galaxy looks like projected on the super galactic
plane. And here is what the corresponding
velocity field's like. There are again two huge attractors.
There's a big one, Hydra-Centaurus, and then there is one on the other side, the
Perseus-Pisces Supercluster. But the flow may continue.
Deeper Redshift surveys suggest that, that in fact this whole local volume is moving
towards an even larger mass concentration, couple hundred mega parsecs out called the
Shapley Concentration of clusters. Named so because Harlow Shapley noticed
that there seems to be excess number of clusters in that are of the sky.
The picture here showing, shows where some of those clusters are in projection, and
they're also close by and large, in three dimensions.
And that's about as large density fluctuation that can cause peculiar
[unknown] as you expect. Not everybody agrees with that, though.
Sasha Kaslinksy and collaborators used distant clusters of galaxies, measuring
their distances from x-rays on, and they concluded that the flow continues even
beyond. They call it the Dark Flow.
Of the face value, this seems to be in contradiction without understanding of
structure formation because we simply not expect that there will be a substantial
loss in build up due to the structure larger than a couple hundreds mega
parsecs. But if this is true, then there must be an
explanation like that. One possibility that people have discussed
is that in fact, there is a huge mass-concentration beyond the horizon of
our universe due to the inflation. We are close at one point but now we don't
see it. But the reason over all gradient in
gravitational potential in that direction and some people called it the tilted
universe. The universe is rolling downhill towards
this unseen hypothetical huge mass concentration, and I'll emphasize the
word, hypothetical. So, to summarize, measuring particular
velocities is very difficult. If you have to use distances to subtract
them directly from observed [unknown] then errors in distances are very important.
And systematic errors that could be present in distance indicator relations
like Their zero point may be function of something could really play havoc with
that. The other possibility is an internally
self consistent solution from a redshift survey alone, but that requires you to
make an assumption about underlying mass distribution models.
We are falling towards Virgo cluster, two or 300 kilometers per second.
And local superclusters falling toward the Hydra-Centaurus about 4 or 500 kilometers
per second. And maybe the whole thing is moving
towards an even larger concentration. But most people think that our net
peculiar velocity, the one that we measure with respect to the cosmic micro
background, is pretty much due to the masses within the 50 mega parsecs for mass
or so. Just not too far from local supercluster.
This is not entirely settled, but it, it is an emerging [unknown] view.
Another important result from analysis like this is that it appears that on large
scales, indeed, the mass and the light are distributed pretty much in the same way.
Galaxies are where the dark matter is. This is not the case of small scales, like
scales of the galaxies, where that there is real a separation.
But scales of large scale structures, this is true.
Because, and we know this because the pecu path there, and peculiar velocities we see
is exactly what we'd expect from the density field.
If the dark matter was associated with galaxies, it was in same general, we
think. Next time we will talk about phenomenon of
biasing and how is clustering evolving in time.