So the sun has joined the main sequence. Let's remind ourselves of what that
means, that means we have a core in which
hydrogen is fusing generating helium. This is supporting the rest of the
envelope by thermal radiation pressure. And there's a theorem that the luminosity
surface temperature, profile, etcetera is all determined essentially by the mass of
the cloud the, the, the ball of hydrogen you're forming. But there are also
dependencies on the composition. What composition, it's hydrogen and
helium. Yes, but there are those trace amounts of
carbon, nitrogen, oxygen. They adjust delicately both the dynamics
of nuclear reactions and of heat transfer, so metallicity makes a
difference. In addition, the rate at which a star rotates can make a
difference, the existence of a close binary partner, some affects of the
atmosphere of the star and when we're observing it also unaccounted for affects
in the interstellar medium can alter a star's appearance.
This, these causes are why the main sequence is not an infinitesimally thin
line, but rather a strip because we have to account for differences in rate of
rotation, composition, etc. And so the, but other than that the star
settles down and sits there in equilibrium and if its a star with the
mass of the sun it will sit there for about ten billion years.
During which time we saw it, things are not exactly static,
there is some evolution going on. What is going on is that the core is
contracting. And the main reason the core is
contracting, you remember, is because of our old equation p is
(n/v)*(kboltzmann)*t. When we take four protons and form an
alpha particle out of them. And in the process eject two positrons
that take two electrons out of the mix. We have gone from a total of eight
particles, four protons and four electrons, to a total of three particles,
one alpha nucleus and two electrons. And,
the net result of this is that the number of particles is decreasing.
If the core does not contract then the pressure will decrease,
pressure can't decrease because it's holding up the external envelope.
There's no real intuitive reason way I can think of to explain this, but the net
result is that the compression and the resulting heating of the core more than
compensate for the decrease in the concentration of hydrogen.
The rate at which fusion is occurring increases and then the core is now
producing more luminosity, more energy, the need to
puff, push more energy through the envelope puffs the envelope out and so
the radius of the star slowly increases and its luminosity slowly increases and
since the rise in temperature of the outer envelope does not track the main
sequence. the star is starting to turn away from
the main sequence if the temperature not changing it's moving vertically up the HR
diagram. And this is where we pick up our story
and where things start to be interesting. So, we meet our Sun at the ripe old age
of about, almost eleven billion years. It has grown somewhat, as we discussed.
It's got a radius of about 1.6 solar radii, it's got a luminosity that's
almost double what it started with. by now it has been accumulating helium in
the core to the extent that the inner 3%, not by volume but by radius.
So, the first point 03 of the solar radius is essentially a chunk of helium
that's, or ball of helium and the helium just sits
there it's inert, it's not producing energy.
Therefore, there's no temperature gradient, there's no flow of energy out
of the helium. So there's no temperature gradient, it's
all at the same temperature, which is the temperature of the hydrogen immediately
adjacent to it and outside this helium core, of course, is a shell of hydrogen
in which fusion is occurring, and that's what's powering the star.
and the rate of fusion in the shell exceeds the rate that was previously
going on in the core. Which is why the star is more luminous
than it was and over these eleven billion years or so, the envelope
has slowly been expanding. And the core has slowly been growing as
helium, hydrogen fuses in the shell, more and more helium is being deposited into
this inert core, which begins to grow. And this is a picture of the solar system
at this point in time, where we are in terms of the sun's main sequence and
evolutionary tract, is that for the first ten and a half billion years of its
existence the sun sat very happily at this point.
And it is now rising away from the main sequence, its luminosity is increasing,
and its temperature is starting to decrease slightly.
As the, envelope puffs out, so the evolutionary track is turning somewhat to
the right. What's the next thing that happens?
Well there is an issue here and the issue is well maybe have an optional clip or
I'll do a calculation associated to this but.
The core being isothermal means again PV is NKT, you need a higher pressure in the
center of the core than at the outside of the core because the center is supporting
the mass, the weight of the outside against gravity.
This means the center of the core has to be more dense than the outside of the
core. Not too complicated a calculation from
this shows you that if the core is too large a fraction of the star, it cannot
support the weight of the outer layers no matter what density you give it and what
this tells you. Is that as the correlate fact-, the
calculation, if you do it in detail, shows you that a core whose mass is more
than 8% of the mass of the star cannot support.
The atmosphere outside it. When the mass of the inert helium core in
the center of the sun exceeds eight% of the solar mass, and it will, remember
that's about the mass of Jupiter. When it exceeds eight% of the solar mass,
it can no longer sustain the weight of the atmosphere and the core starts to
collapse. Collapse rapidly.
What is rapidly? Rapidly means on the gravitational
scales, tens of millions of years. Does, that was this Kelvin-Helmholtz
Scale we talked about. So the core starts to collapse rapidly.
This releases, of course, a great deal of Kelvin-Helmholtz gravitational potential
energy. It also compresses the hydrogen burning
shell immediately outside the core, because that falls in as the core
collapses. This in turn, increases the luminosity
that, that hydrogen shell is putting out. That puffs out the star's atmosphere and
cools it down and the result. Is that the envelope has puffed up.
It's radius is larger, the external temperature decreases, so the star starts
moving to the right along the HR diagram. This is what the solar system will look
like with a larger, cooler sun. notice the time, 700 million years have
elapsed. And the sun is now a sub giant star, it
is moving, it'll spend these 700 million years moving to the left and slightly
heating up. Moving to the right, sorry.
So, cooling down and slightly increasing in luminosity.
As the envelope puffs up. What's a subgiant star?
Well, an example of a subgiant star is Procyon in Canis Minor.
you can look up its data, that's a good example of a subgiant star.
Notice, the Sun will only last about 700 million years as a subgiant whereas, it
lasted ten billion as a main sequence star.
Subgiants are more rare, but because they are luminous, notice they are, the Sun
will be more luminous at the end of its subgiant phase we can see some of them.
So we've left our core collapsing. What does that do?
Well, once the core starts to collapse, then compression heats the shell,
luminosity of the hydrogen fusion shell increases dramatically, this puffs up the
envelope. As it puffs up it cools out cools down it
cools down to a temperature of a few 1,000 degrees where
Negative hydrogen ion opacity again controls the opacity of the external
atmosphere. So it's approaching that Hiachi
temperature that we talked about, because the external atmosphere is opaque.
That means that instead of radiation transfer at the outer atmosphere, we have
sort of deep convection cells over here. These dredge up to the surface the
products of early fusion in the core. And we see a change in the spectrum of
the star. What comes up, well.
Trace amounts of carbon, nitrogen, and oxygen, whose isotopic abundances have
been slightly shifted by the the CNO processes that have been
going on I'll be at, at a smaller rate in the interior of the star in a bigger
star. We'd see the sea in no abundances
that are adjusted by the action of the CNO cycle.
Now whenever a star puffs up this large, note the sun is acquiring a radius of 160
solar radii, it's doing it rather quickly within about 600 million years.
This quick puffing up is always accompanied by enhanced stellar wind and
mass loss. Notice that the outer layers are now much
farther from the center that they were. Much less strongly gravitationally bound.
So the sun at this point might loose as much as 28% of it's mass in it's red
giant phase. The way this would look in the solar
system, is that poor Mercury will have completely been subsumed in the sun.
Venus and Earth still exist I'll be it temperatures there would be very hot
what's an example of a red giant that we know well the star that we call al
debaron and probably should call a dubron is a red giant with 1.7 solar masses so
its a slightly more massive than the sun red giant with a luminosity about 500
times that of the sun in fact at the peak of its red giant phase and we'll talk
about that the sun with have a luminosity over 2,000 times the correct solar
luminosity and so the sun is puffing up cooling down.
And this goes on, and the core is collapsing.
Now, neither the puffing up and cooling down can go on forever, nor for that
matter can the core collapsing. So.
Something's going to stop the core collapse.
And remember that thermodynamic pressure is not able to do this because of this
Schoenberg-Chandrasekhar limit Before we go there let's remind ourselves where we
are on the HR diagram. We have finished the sub giant phase and
we are now climbing the red giant phase. And this phase is the phase that will
last for the next 600 million years or so.
and the sun becomes more and more bright, more and more luminous at a pretty
constant temperature determined as I said by H minus ionization.
And then what. Well first of all the court cannot
continue to collapse its. Collapses stopped by a quantum effect
called electron degeneracy pressure will meet this effect again and while we
haven't done much quantum mechanics we can explain some of it.
electron degeneracy is the result of the poly exclusion principle.
Which remember tells you that only one electron or two if you account for a spin
states, can occupy a given state. And there is a finite number of electron
states up to a given energy in any volume of space.
This electron degeneracy, if you want, is the reason why when I clap my hands they
don't go through each other. Although low lying states in this region
of space are occupied. All of these electrons would have to be
excited to higher energy states. The neat thing about this is it has
nothing to do with temperature. Even if you have zero temperature,
electrons are all at the lowest possible state.
If you try to squeeze too many of them into too small a volume, some of them
have to. Reach excited states even at zero
temperature. So what this does is it produces a
temperature independent contribution to the pressure.
When you try to squeeze system with electrons in it too tight one of the
things you're doing. It's, you're squeezing some electrons
into higher energy states. In normal systems, this is not, in normal
gases this is an irrelevant contribution, even at the center of the sun.
You can make a calculation that it's less than a fraction of a percent of the total
pressure at the center of the sun. But when this degenerate helium core,
when this helium core collapses, its density becomes so high that in fact.
Electron degeneracy pressure is what ends up supporting the sun's atmosphere.
And what is going on is that, The degeneracy pressure, as I said, is
temperature independent. But it's very strongly dependent on
density. It increases as the density^(5/3).
The constant, ke, is slightly dependent on the details of the model.
And for the parameters relevant to the sun I gave it here.
You plug it in, as I said, you'd find that the sun is highly non-degenerate
today. But that the helium core will become
degenerate, and this is what will cease its collapse.
The important thing about degenerate matter is that.
Its pressure is independent of temperature.
If you heat a gas, it will expand because when T goes up P goes up.
When you heat a degenerate gas it will not expand because P is completely
independent of T, until thermal pressure grows enough to overtake degeneracy
pressure. So this will stop the course collapse it
will stop when it reached degeneracy. What does that do to the outside of the
sun, we'll see in the next clip.