Finally, let us now see why spiral
galaxies are spiral.
Obviously, the spiral arms are the
defining feature, and there are some
important observational facts about.
Probably, the most significant of them is
that they're seen only in disks that do
contain interstellar material, the gas,
which then causes star formation.
There's.
Disks which do not contain much gas, those
are the S0 galaxies.
Another important clue is that they're
seen in young stars, and since young stars
tend to last less than full rotational
period, it suggests that.
Possibly, that spiral arms are transient
phenomenon, that they actually last less
than typical rotations of, of, these
galaxies.
And, something that's a little tricky is
that when you look at the spiral galaxy,
you have the impression of a vortex, and
that they.
Rotate in a sense of you would see, in
say, water going down the sink.
They knew except that they move at half
the angular speed of the disk.
So the disk of the galaxy rotates in the
same direction as you'd infer from binding
of the arms and so do the spiral arms but
at half the speed.
So a relative of the disk, the spiral arms
are actually moving in the other
direction.
They move as either scooping up the stars
counter intuitive to what you think.
Think.
Now the important feature to remember here
is that essentially all galactic disks
have more or less flat rotation curves,
meaning the linear velocity is roughly
constant as a function of radius.
Which means that the angular velocity goes
as 1 over the radius.
And so if you were to start with say
straight, features directly through the
galactic center due to the differential
rotation it will naturally produce
something that looks like segments of
spiral arms.
Which actually presented a dilemma
initially on, because if somehow spiral
arms were constant because of the
differential rotation they'll keep winding
and winding until they look like a really
tightly wound spiral, and that's not what
we see.
An interesting way to approach this is as
follows.
Imagine that stars move around center of a
galaxy in elliptical orbits because
roughly they do.
But its sub, subsequent orbits of larger
radii are shifted a little bit.
So it kind of looks like this.
You start with 1, then keep adding,
concentric but tilted orbits.
And by the time you're done.
You can see that there is something that
looks like two spiral arms.
And in fact, this is roughly what happens,
but the only, the question is, why?
The answer why, is the so-called density
wave theory, that was developed in 1960s
and 70s by Lin, Shu [unknown] and others,
and the upshot is that spiral arms are
density waves in deferentially rotating
disks.
If you were say to drop a rock in a pond
it will have circular waves going away
from the center.
But, galaxies are not stationary points
and if you are to make a prediction/g in a
deferentially rotating disk like disk of
spirals, what you get is not circular
waves but spiral waves.
The reason why they persist at all Is
resonant motions.
You can decompose motion of any star
around center of a galaxy to first
approximation as circular orbit with some
perturbation.
And the perturbation can again be
approximated as, see a star wobbling
around at radius, in other words, making
circular orbits, around some hypothetical
node on the central part of the orbit.
That resembles epicycles, from Ptolemaic
theory of solar system.
And in fact those are called epicycles.
So if you.
Have the exact match in the numbers of
orbits, around, at center of the epicycle,
and its motion around center of a galaxy.
We will have amplification, and that is
exactly what's happening.
So if you look at angular frequencies,
omega not to be confused with density
parameter.
And then look at the epicyclic frequency.
Again angular frequency then divided by
integer number which is usually small one.
One or two or something.
Then the first two resonances are called
the[UNKNOWN] resonances.
And they actually are the radii in which
that Particular rotational frequency
occurs from which or to which spiral arms
extend and since usually the 1st harmonic
the first of residence is the strongest
one this is why we mostly see two arm
spirals although we do see for example 4
arms spirals and so on.
So another way to phrase this is that
spiral's arms are density waves which are
really resonances of perturbations in
these differentially rotating disks.
So remember the orbit crowding diagram
that is more or less what happens here
where unelliptical orbit is can be really
be composed as circle plus an epicycle
that makes exactly one turn.
As the big one turns around, and so that,
that causes the elliptical shape.
Now the orbit crowding really implies that
there is going to be a density pile up,
and that's exactly what spiral arms are.
Now these waves are moving relative to the
underlying disk gas and stars.
And so, as the waves hit material, they
are compressing it.
Compressed gas.
Is liable to make stars, which is why we
see star formation associated with spiral
arms.
So this is why star formation can be
triggered by spiral density waves.
That's not the only way in which we can
trigger star formation disks, but
obviously it works.
And there'll be stars made of all
different.
Masses, but the most massive stars, as you
probably know, are the more luminous ones,
and they live the shortest.
So it's the shortest lived, most luminous
stars, which haven't had chance to, drift
away, from the wave, before they explode.
That will deleniate, pattern on spiral
density waves.
When you look at bluer light ones, which
are more susceptible to the radiation from
Yankov/g luminous stars, you see very
prominent spiral density patterns.
If you look to the redder light ones.
Say, near infrared, where the dens, where
the light is dominated by the older, red
giant stars.
The spiral arms are still prominent, the
density wave is still there, but not
nearly as much, or not nearly as sharp as
you would see in blue or ultraviolet
light.
Flight.
So schematically, you'd expect things to
look like this.
There is the spiral density wave that
moves relative to the underlying disk, in
the opposite way of what you think from
say, water going down the sink.
In other words, the arms are scooping up
the materials so the leading edge of the
waves is the inner part of the spiral.
This is where density wave compresses the
gas, molecular clouds.
Makes dust lanes.
And then, inside of them, there'll be star
formation.
So you expect to see dark lanes on the
leading edge, which is back-, back side of
the spiral arms.
Followed immediately by regions of star
formation and then kind of more diffused
stellar population as you go towards the
trailing edge.
And now let's look what that looks like in
real life.
So this is a picture from Hubble space
telescope of, I believe N101 right near my
spiral, and this is exactly what you see.
The inner part, which is the leading edge
of the spiral arm, is where you see the
dust lines, and then the red, dots and
blobs that you see in the dust lines are
immediately.
Past them, or the regions of young star
formations.
Those are H alpha, nebuli ionized by young
stars.
The young stars burn out through the dust,
dissipated, and then you see luminous,
blue, stellar light.
And then kind of fades away as you go
towards the trailing edge of the spiral.
So the theory predicts exactly this.
So to summarize spiral arms are density
waves that occur in deferentially rotating
stellar disks.
They will compress gas that will lead to
star formation at edges where gas enters
the spiral density wave.
Stars themselves will simply pass through
density wave.
Just like water molecules pass nicely
through waves in water.
And this dynamical theory is, is very
successful in explaining the global
properties of spiral galaxies, but it's
not perfect.
First of all it doesn't say why were there
waves to begin with.
Some sort of disturbance has to happen and
one possibility is that encounters between
galaxies Create such a disturbance.
That's entirely possible.
Another part, which is a little more
difficult, is that not all spirals are
perfect alarm spirals.
They're detached spiral arms, spurs,
things like that.
So additional mechanisms might be
responsible for a creation of Such
patterns.
Now where the theory predicts exactly what
we should see in say, a two arm grand
design spiral, as they're called.
Here are other types of these galaxies,
spiral so to speak, in which, the patterns
are much more diffuse and they're both
flocculent galaxies that they almost have
no spiral arms, but they certainly have
patches of star formation.
And even maybe little segments.
They may be caused by different
phenomenon.
Namely differential stretching just like
we addressed at the beginning of the
lecture.
So that's it for these galaxies.
Next, we will start talking about
elliptical galaxies.