Okay. We figured out when it happened.
Now what? we're going to go back four and a half
billion years ago. The atoms that currently comprise the
solar system are already around in this part of the cosmos.
How those atoms were created, where they came from, we'll think later.
The question now is, in what form were they likely to be found?
And, over the past few decades we have a pretty good idea of what that form is.
the material that currently forms the solar system was probably found in a
large molecular cloud. What's a molecular cloud?
Oh, it's a great big collection of, as we know, mostly hydrogen with some
contamination, traces of other elements. it's called molecular if it's cool enough
that hydrogen atoms actually form stable bonds and we have hydrogen molecules in
it. And inside this molecular, wait a minute.
This is already a problem. And it's a problem that I want to pay
attention to, because this is a problem that will haunt us through the rest of
the class. The problem is gravity.
And the problem is that the idea of a large cloud of hydrogen floating around
in space, on the face of it, makes no sense.
Because if you're an atom in the center of a cloud of hydrogen, then of course
you're attracted to all other atoms in the cloud.
And the net attraction on you if the cloud is reasonably symmetric might be
zero. Fair enough.
But if you're an atom near the edge of the cloud then clearly the net effect of
gravity is to attract you towards the center.
Gravity applies a pressure, a contracting pressure to every object.
And whenever we see something in the universe that is not collapsing and
crunching down to a point, something must be holding it up.
What holds up a molecular cloud? Well, it turns out that a molecular cloud
is held up simply by thermal pressures. This molecule near the edge of the cloud
may indeed be accelerated towards the center, but on its way there, it
encounters other molecules which have random thermal velocities, it scatters
off of them, and eventually never gets anywhere.
The cloud, the general shape of the cloud can sustain itself, and we can do a
really nice order of magnitude calculation to understand what the
conditions in a cloud must be in order for it to sustain itself.
And the way we think about it is that if we have a cloud, then we know that the
average kinetic energy if a molecule say, so m would be the mass of a hydrogen
molecule and the cloud is on the order, there may be factors of two or three that
I'm skipping, of k Boltzmann times the temperature.
And on the other hand, the typical gravitational velocity associated to this
cloud can be estimated from the escape velocity, if a molecule is moving with
the escape velocity then it's not really bound to the cloud it can escape.
And the escape velocity we computed is again on the order of newton's constant
time the mass of the cloud. Divided by, the year distance from the
effective center. So R might be.
The radius of the cloud would be a typical number to enter.
And now if this velocity and this velocity are of similar orders of
magnitude then one can imagine that the thermal fluctuations in the cloud are
about the same order as the gravitational pressure.
This will tell us that the cloud can sustain itself under pressure.
This is how molecular clouds survive. The denser a cloud, the higher its
temperature must be in order to prevent the gas from collapsing.
So now we understand that you can have a molecular cloud sitting there.
There is still a problem with gravity and this is a problem that is unique to
gravity in contrast to other forces. And the problem that occurs with gravity
is that imagine that through some reason and we'll talk about it later, this
region of the cloud becomes denser. If this region becomes a little bit
denser than other regions, then of course the net gravitational attraction
everywhere is slightly more directed toward this region of the cloud.
If the net fluctuation is large enough compared to the temperature, that in fact
some significant infall occurs, well the net, then more mass will fall onto this
region. This region will become denser still.
Becoming denser still, the collapse will become more significant.
In other words, once you have a fluctuation or some reason, an additional
den- extra dense region in a cloud. Because unlike, say, electromagnetism,
where if you charge some region with positive charge, it'll attract negative
charge and neutralize itself. And enhanced mass density attracts mass,
which increases the enhanced mass density.
Gravitational collapse is a runaway process.
Even if the cloud is holding itself under thermal pressure, the situation is
unstable. If you make a sufficiently large
perturbation, the cloud will collapse. And this is what happened to our
molecular cloud that led to the formation of the solar system.
So what caused one region of the cloud to be dense?
Well, we think it was the shock wave created by the explosion of a supernova.
In fact, probably more than one nearby and we'll see how that might have
happened, again, later in the class. This causes the great big cloud to break
up into fragments and triggers the collapse of these fragments.
The fragment that created our solar system was probably on the order of
magnitude of 20, 2 to 20,000 astronomical units in size abd with a mass of about
3,000 solar masses. this did not create the solar system, in
fact, it created a cluster between 1 and 10,000 stars.
So, the condition that we see in the solar system suggest that the sun was
formed as part of an open cluster like the Pleiades.
It's now not bound gravitationally to nearby stars and so it's not part of a
cluster. This cluster has dispersed and in fact,
this is the, this leaves a reasonably recent insight that the sun forms as part
of a cluster and the search is on in the neighboring part of the Milky Way to find
the stars that were once members of our cluster.
I do not know that there has been success so far.
And again the shock wave triggers. Remember, it's a sound wave.
There's a region of high pressure in the cloud.
That region becomes sufficiently dense that gravity overcomes thermal pressure.
This is called the Jeans Instability. It's the fact that if you have a
fluctuation, it will grow, and as we saw, If you have a fluctuation whos mass
relative to the is related to the temperature by this equation where big M
is the mass of the cloud say, or the region that's collapsing and little M the
mass of the constituent particles. If you satisfy this condition,
then the region will collapse. And this is the Jeans condition.
And any object that is not collapsing that's made of gas, will have to obey
stability condition against this collapse.
And larger objects, the condition might change, but everything in the universe
that is not collapsing is held up against gravity by something.
That's the light motif that I want you to take away from this.
So. we have this, large molecular cloud and
it initiates a collapse. In this simulation,
what we're going to see is how the collapse of a molecular cloud looks.
On the left, we see the density. On the right, the temperature.
There's some region of increased density. The cloud is collapsing towards the
region of increased density. localized regions of high temperature are
forming. The timescale here is tens or hundreds of
millions of years. We see the beginning of stars forming.
We see these explosives, explosive supernovae, and we see that after a
supernova, there's local, flux of sudden star formation.
Look at that big super nova and then the sudden concentration of star formation
near it. So this is presumably what happened to
us. The sun was formed as one of these
clusters that were generated or triggered by an explosion of a nearby supernova.
We'll get back to the star part of it. But first, we have our cloud, it's about
200, 2000 astronomical units to aside, and it starts to collapse.
But now, let us focus our attention on the region immediately near us in the
cloud, immediately near where we are now. So somewhere there, we will zoom in, and
look at a region of maybe 200 astronomical units or 1,000 astronomical
units around where we are now, that region begins to collapse under the
weight of it's own gravity because the fluctuation makes it too dense for
temperature to sustain it. What happens when a cloud starts to
collapse? Well, first thing we understand is that
as the size of the cloud gets smaller, any random rotation that the thermal
motion, or whatever, might have included is going to get sped up by the
conservation of angular momentum as this demo brilliantly shows.
So what the demo showed us, is that whatever random rotation was part of the
thermal motion of this huge 20,000 astronomical unit sized cloud.
as the cloud collapses, is accelerated. And what we find is that the whole cloud
is spinning rapidly. Now it's not spinning rigidly, because
it's not a piece of plastic hooked up. These are independent particles of gas.
But the net result is the same. The rotation is enhanced. This is the
rotation that makes the planet's orbit, the sun in the same direction as the sun
rotates there was an overall rotation present and it was enhanced by collapse.
This is another important result which is that objects that are collapsing as they
come closer to the center and that such a direction that they're coming closer to
the axis of rotation by the conservation of angular momentum, NVR being conserved
means that as R shrinks their velocity, their speed has to increase, these
objects have to move faster. This creates a barrier that prevents the
cloud from collapsing into its axis. On the other hand, collapse in the
direction along the axis, the other direction is uninhibited by this.
And so, the cloud collapses far more readily along the axis than perpendicular
to the axis. The net result is, that what was once
probably a roughly spherical cloud is flattened into a pancake shape.
This is the reason that we find the planets all orbiting the Sun in roughly a
plane. The plane of the ecliptic is the plane perpendicular to the original axis
that was randomly the axis of rotation, the neck rotation of a cloud.
And then within about 100,000 years of the initial super nova trigger, the cloud
is contracted to a radius of about 200 astronomical units.
And it's now flattened into what we called a proto planetary disc.
A cloud of dust and gas Here is a nice infrared image of such a
protoplanetary disk in the Orion nebula. And here's a sequence of nice Hubble
images that show us how this takes place. So here we see an image of Orion's dagger
with the Orion nebula in the center. And as I click, we will go through
increasing magnifications. we magnify.
Here's a magnified view of the nebula. In the center of the nebula we find all
these dust clouds. And in them we find these cocoons in
which stars are formed. And upon magnification the infrared image
shows us very nicely the nascent star in the center surrounded by a protoplanetary
disk. It's happening there.
physics is universal, this is the way it happened here.
In addition to spinning up, another process that begins to take it place as
the solar nebula collapses, is a process called Kelvin-Helmholtz heating.
This involves the fact that some of the gravitational potential energy,
liberating by all this stuff falling in towards the center is indeed converted
into rotational kinetic energy. But most of it is distributed by
collisions into heat and into the random motion of the components around them.
So as an object contracts under the form of gravity, it's gravitational potential
energy's being converted into heat, and the temperature therefore rises.
this sets up a profile, a distribution around the disc where of course the
density is largest at the center of the disk and tapers off to the edges.
And likewise the temperature, the most compression has taken place in the
center, so the temperature near the center of the disk eventually reaches
2,000 Kelvin. And when it does, we'll see that a
surface, next week we'll see that a surface with a temperature of about 2,000
kelvin sort of stabilizes the material inside it is the protosun.
Most of that will eventually be the Sun, what's left outside is the remnants that
will become the rest of the solar system. And so in the center the temperatures
very high and the densities are rising and then both density and pressure
decrease as you move outside. And so you have this disk with hydrogen,
helium and some of 'em, some other materials.
in this region where both temperature and density.
Decrease with R with distance from the center, and this will have some serious
impact on the state in which we might find different components of the solar
nebula. Farther out we have essentially very
small density, very small pressure, and very cold temperatures.
Near the middle it is hot and relatively denser.
Let's see interesting demonstration, of how this
effects the situation. One of the important ingredients in the
solar nebula is water. Hydrogen and oxygen find to form water.
And remembering that it's despite, the increased density from collapse.
Under very low pressure compared to the atmospheric pressure we feel on earth.
We need to understand how water behaves in space and so what we've done here is
we've taken some water colored blue so we can see it and place it in a vacuum
chamber and essentially we're simulating the conditions in space.
The temperature is room temperature and the water is boiling.
We know, anybody that cooks knows, that as you go to higher altitude, it's lower
pressure. Water boils at a lower temperature.
Here the water is boiling at room temperature.
Boiling water is converting liquid to water vapor.
That requires an input of latent heat. When we boil water on the stove, that
heat comes from the stove. Here, as when our sweat evaporates from
our bodies, it's coming from the water itself and that's cooling the water down.
We see that the boiling is slowing down, because, as more water evaporates, the
water is in fact, becoming quite cold. And when it becomes cold enough, what we
observe is that the boiling completely ceases, the water has frozen.
what we've produced, when we take it out, is an ice pack.
Essentially what we're learning, is that, at the low pressures obtaining in space,
water can exist as ice, or as water vapor but not as liquid water.
The answer to the question is there water on Mars or on the moon or in space in a
silly sense is no. You can have ice and you can have water
vapor, you can not have liquid water at the low pressures obtaining in space.
This is, something we're familiar with for example carbon dioxide, exists on
earth as vapor, and is solid, but not as a liquid.
It's true for any substance that's sufficiently low pressure.
And if the pressure's in space, it's true for all substances.
Cannot resist the temptation to demonstrate that with nitrogen, a major
component of air, so here we have liquid nitrogen.
It is boiling because the boiling point of nitrogen is negative 100 degrees
centigrade. We put it in the vacuum chamber.
We evacuate. And again, we see that the nitrogen boils
even more vigorously and as it boils even more vigorously at the low pressures,
it's cooling itself down and like the water, eventually, nitrogen freezes.
The freezing point is only a few degrees lower than the boiling point, but what we
have there is solid nitrogen. Where we see in this simulation,
is the impact that the temperature gradient through the nebula, will have on
the state of various materials or various of the metals that are present in the
nebula. We see that, as we said, the temperature
near the center near the, the outside of the proto sun, reaches close to 2,000
degrees. On the other hand, as one moves further
out, the temperature decreases. And what we see is that as the
temperature decreases some materials over here on the right, transition from gas to
solid, notice there are no liquids, many oxides and metallic iron for example are
solid at temperatures below 1300 degrees and so that is the temperature that
obtains near the current position of mercury.
How farther out where Earth is located. other minerals
made of, iron and, sulfur, for example, are, solids, but water is still a gas.
Water becomes a solid at a temperature of 175 degrees K, and the line at which
water, a much more plentiful material than, say, iron or nickel, because
remember that, graph of abundance is, was declining on a logarithmic scale.
Water, made up of hydrogen and oxygen, is relatively light elements.
They're relatively plentiful. water becomes solid just inside Jupiter's
orbit. Perhaps not a coincidence, and then
farther out, ammonia and methane, become solid somewhere between Saturn's orbit
and Uranus' orbit, and argon and neon noble gases are solid farther out.
What we see is that as you go farther out into the nebula, there are more solids,
and this will have an important impact on, planet formation.
What we've seen is that, the fact that temperature and density depend on
distance out in the nebula, will mean that the form in which various
materials or constituents of the nebula are likely to be found will change closer
to the center we only find gases. As you move farther and farther out, more
and more of the materials are going to be solids and we saw that in the center
we're forming this protosun. The protosun will eventually become the
sun the region enclosed within this boundary of temperature 2000 Kelvin.
Most of that will turn into the sun and that in addition to providing us life
further on, such as ticking time clock for processes
going on in this disc, full of, gas and in the outer reaches will be called dust,
microscopic particles of solids. the ticking clock is, that within about
ten million years, the sun will ignite as a star.
When that happens, the stellar wind, the solar wind that we discussed undergoes a
very intense period where, for a few million years, the solar wind is
extremely intense, a few tens of millions of years.
This is called the T-Tauri winds. Star in this stage are called T-Tauri
stars. The sun was once a T-Tauri star.
And, the stellar wind, the pressure of this stream of charge particles is so
large that any remaining gas and dust is completely blown away from the system.
And so, that gas and dust is to form planets and whatever else it wants to
form. The timing is 10,000,000 years.
What hasn't formed in 10,000,000 years is going to be blown away.
Gas and dust cannot survive the solar wind although more heavier more robust
objects are able to survive. Here's a nice demonstration.
Of how things look from the point of view of producing the
star, what we are going to do again is right density here, density is common
density, so it is density throughout the depth of the nebula.
We're seeing a two dimensional image and as time increases we see both density and
temperature increase. And we see in the middle the formation of
the protosun the red line indicates a temperature of 2000 degrees.
This is where the protosun move forward and it's still surrounded by the proto,
planetary disc where soon our planets and us will come into being.
We'll start that process in the next clip.