This content explains the stellar evolution process from main-sequence stars to red giants, detailing the internal changes and the subsequent emergence of variable stars, particularly Cepheids, which are crucial for measuring cosmic distances.
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Folks, let's begin. Uh, we now want to
start to talk about giants. So, we spent
the last lecture focusing on the main
sequence stars and then you know they're
in the core they're converting the
hydrogen into helium and so the question
becomes what happens when that process
is completed when all the hydrogen has
been converted to helium and of course
that's where we uh enter into the giant phase.
phase.
So let's just start off here. Uh label
completed. Okay, in a nutshell, the
steps uh look like this.
So, and we've really kind of broken them down
down
here, glossing over a lot of the
details. So, step one, uh, the core is
Um, and then once it's helium, you have
no more uh hydrogen to fuse. So that
means that you're going to stop the
fusion stops. So if you have then the no
more core fusion, you're not producing
any more photons. So you no longer have
those that photon pressure that's
traveling outward away from the core.
And so what that means is gravity now is
stronger because you don't have any
repulsive, you know, photon pressure. So
gravity can go ahead and begin to
So
remember fusion is only happening in the core
core
uh when we're on main sequence in in
there you have the hydrogen is being
fused to form helium and eventually
that's all used all the hydrogen is used
up and then the core becomes completely
helium and so then the hydrogen fusion
in the core
stops no more photons
um photon pressure radiating outward to
halt the compressive effects of gravity.
So then what gravity does is a thin
spherical shell of hydrogen just above
that helium core and the gravity um
compresses it and eventually it's going
and temperature. And again, this is
gravity is squeezing that thin spherical
shell of hydrogen and it's going to get
it above 10 million Kelvin and boom,
that hydrogen shell is going to begin to
fuse. Hydrogen shell just above the
temperature
reaches 10 million or around 10 million
tilda on that.
that. Okay.
Okay. And
And thus
fusion
begins. I should draw a
picture. Okay. Now you're going to have
the photons are going to be produced. So
you're going to have photon pressure
that's going to radiate outward and that then
then
pushes greatly on the outer regions of
the star and that's what expands it and
and that's how the giant forms. So let's
see I was on uh step four. So step five
line up my pages here.
here.
uh
begins because you got the
and it dominates which means it's stronger
stronger dominates
star is expanded and it's expanding
because that photon pressure is greater
than gravity and it's pushing the outer
regions of the star
away. Well, anytime you take a gas and
you expand it, then that gas temperature
is going to drop. And so in the outer
region of the star, the surface
temperature will drop. So we're on the
number six
surface,
Kelvin. This forms what we call then a red
giant. So in five billion years our sun
because our sun has a mass greater than
40% the mass of our sun. I mean it's
100%. Um our sun is going to become a
red giant through these steps that we've
just outlined. So it mean five billion years.
years.
So in
about 5 billion
son will
giant. Giant because you have not core
fusion happening but shell fusion and
that that elevates the photon pressure
to greater values throughout the volume
of the star and so hence it's stronger
than gravity and can push away the outer
regions that will cool those outer
regions the drop down comet colors given
off will be in the red the orange and
that's where you get the term red giant
let's uh draw a picture
here I tell you what I'm going to draw
it on another page
because I want to have plenty of
uh surface. So, I'm going to go to my
page three. Move that out of the way.
And I want to draw the picture of the red
red
giant. All right. So, what we got to
draw some circles
here. Okay. So, draw a circle
there and then above that circle
Okay. And we will label this red
giant. All right. So, we got to talk
about what's happening. So, in here in
the center, that's the core. That's just
helium. And it's inert. It's not doing
anything. It's just sitting there.
There's no fusion. So,
Okay. Then right above that helium core
is this thin spherical shell of
hydrogen. It's above 10 million Kelvin.
It's fusing. So we're going to label this
this
hydrogen
Then this region here is again just
Now because the photons are produced in
this spherical
uh shell instead of in the center
they're much stronger for a given
distance away. Hence there's greater
than gravity. Hence that's what pushes
the outer regions and that's what makes
it a giant. Okay. But the only place
that we have the fusion happening here
is in this thin spherical shell of
hydrogen. Now of course the byproduct is
helium. So, it's dumping that helium on
this inert helium core. So, this helium
core will actually grow in mass, helium
mass, because that's where the helium is
going to get dumped on. But this is the
sort of picture that you should think
about in your mind when you think about
giant. All
right, move this up. Next bullet. Let's
get into what happens
uh eventually in the core. And
eventually in the
core, this is going to get hot enough
that it's going to begin to fuse. Okay.
eventually the
core will
temperature. The reason it does is you
have the the hydrogen shell fusion which
is producing a tremendous number of
gammaray photons. So think of that as energy.
energy.
A lot of that energy of course travels
outward but then some of it is inward
and will heat up this core. So
eventually the inert helium core will
reach a temperature of 100 million
Kelvin. So till the about 100
100 million
Kelvin. If you have helium at a
temperature of 100 million Kelvin, it
will begin to fuse and it forms two
products and those two products are
carbon and oxygen. So we're going to
look at those
processes. So we have in the way that
I'm just, you know, sketch this out. So
here's what happens. So you have uh
ordinary helium. So, helium 4 plus and
these are the nuclei. Another helium and another
another
helium. So, that's 12. That'll give us
energy. So, one of the products of
helium fusion is carbon. This is
So there's 12
particles, you know, two protons, two
neutrons, two protons, two neutrons, two
protons, two neutrons, six protons, six
neutrons. Okay, that's carbon. And then
what happens is you got a carbon then'll
get bombarded with another helium and
that'll produce oxygen. So you also have
some of that
C12 gets hit uh with a helium 4. Oh,
another name for helium 4, by the way,
is an alpha
particle. Maybe should I I should write
that down? So 12 + 4 is 16. So eight
protons, eight neutrons, and
oxygen. Okay. Now
um so just to in your notes, alpha particle
is
Okay. The fusion of helium in the core
happens very suddenly in this event we
fusion helium
flash. Helium
flash technically because it's in the
core they'll call it helium core
flash. So sometimes
helium I'll just put in here parentheses core
flash. Okay.
So, so again 100 million Kelvin is the
required temperature to go ahead and
fuse the helium and the products are
energy and carbon and oxygen. Okay, so
that you're now producing in the core of
that giant star carbon and oxygen. So we
rewind wind ourselves back. To fuse
hydrogen, which happens in main
sequence, you only need a temperature of
above 10 million Kelvin. To fuse helium,
you need a temperature of
100 million Kelvin. Oh, get up there.
are helium core
I'm going to draw the picture just so
Okay. So, again, we're back to a giant
star, but it's hot enough in the core
that we've got the uh helium core fusion
occurring. So, giant
core fusion. All right. So now just to kind
kind
core helium
fusion, it's
producing carbon and oxygen. So you're
going to slowly build up carbon and
oxygen in there. So helium fusion in the
core and we're getting carbon,
carbon,
oxygen, and of course energy. most
photons. Then the shell above that just like
hydrogen
shell. Let me move this
up. Fusion I want to put temps here.
Temp of the core is on the order of 100
100
million Kelvin and the temperature of
that shell right above it is on the
order of
10 million Kelvin and then out here you
have inert hydrogen and helium. So you
have no fusion occurring here only
fusion is in the shell and in the core. So
inert
Okay. All
right. Next
Let me step
back. You're on main sequence. The stars
exhausted all the hydrogen in the core.
And then we go through the processes
that we just outlined at the beginning
of the
lecture. Steps one, two, and three,
four. So what's going to happen now is
you're going to track off a main sequence.
sequence. So
sequence. Post you know meaning like
after. So
sequence. So what happens is the stars
then are going to leave the main
sequence line and they're going to
travel to the right and upward. So
line and
and
track upward and rightward.
picture and write word, you know, the
upper right portion of the HR diagram. So,
So,
here. And there's main
sequence in
um luminosity versus color or
wavelength. Okay.
color
luminosity brightness
whatever it's just our standard H chart
line so you've got to have the star has
to be have a mass greater than 40% the
mass of our sun so not down here but up
here and then then they all are going to
walk off of this line and they're going
upward depending on where they started
out on main
sequence. Okay? Because they got a head up
up
here in this
region. Okay? So they this is main
sequence. They leave this and then
travel upward. Now if we look I titled this
this
discussion variable
stars. So it is they are a variable star
when the following occurs when they
leave main sequence and as they migrate
up to the land of giants. So in this
region they're this is what we mean by a
variable star. I'm going to
excursion and what we mean by the
excursion leaving the main sequence line
and traveling up to where the giants and
the super giants are. Um so during this
excursion a
star can become
unstable and what happens is you get a
fluctuation in the luminosity. So that's
what we mean by unstable
will
vary. So an so another this path then right
right
here that's sometimes called the
instability strip. So the
strip. So I'm going to label this.
That's this region right here. This is
the instability
strip. Star that's in
star. Now,
uh they actually set down in there in
two regions and we want to talk about
there's there's a lower region and an upper
upper
of instability.
Okay. So we have um
are
called I'm going to draw a picture
ray
variables that's a long word
word ray
ray
variables higher mass protein flash
Se variables. Some people just say RL
and others just say C and you don't say
the word variables. Okay. So, let me go
back and draw another picture. So, and
go back back to our HR diagram. Da da da
sequence line. Na na na instability
strip there. Na na na. And then here's
where they set up these and these. So
these are the seafids because they have
higher mass. They're up. The mass
here. And when they're there, they're
pulsating. The luminosity is changing.
Now I want to start a new bullet because
the reason that we're wanting to hit on
this is very important is these seafoods
are very important. There's something
very magical about them that we use and
so they're worthy of a discussions
themselves. So new bullet here
eight seafoods which is short for secret variables.
variables. So,
seafoods
pulsation pattern. And I want you to
remember this. So, if I go
back here, a star can become unstable.
Luminosity will vary. That's you know
another way for that is uh another word
is pulsation. Okay, you know bright dim
bright dim. Okay, but the way that the
seafood does is kind of kind of unique.
Okay, so you have to remember this. So
it's a very rapid brightening and then
brightening followed by a gradual [Music]
dimming. I'm going to draw a
picture and this would be luminosity as
a function of
time. So we're watching the star and so
what so what you'll
see looking at a seaf what you'll see is
the following. So it'll go
uh rapid brightening and then this
gradual dimming. So you see it shoot way
up and then it a long tail down and then
up very quickly and then long tail down
and then up very quickly and then a long
tail down. That's the sort of pattern.
here. You see because this is time. So
this is a very narrow band of time. It
quickly gets bright and then it slowly
dims. So this is the gradual dimming
down here. This part.
Okay. So you see kind of that saw to
pattern. Okay. Now, it turns out that
relationship between the average
luminosity and the length of the pulsation
pulsation
period. Okay? So, what they do is
they're going to time out the length of
the pulsation period and then they can
get very accurately an uh absolute
magnitude or luminosity. And so, then we
can use that to estimate distance.
So um by [Music]
Determine absolute magnitude or the
luminosity. So let me draw here. So the
pulsation period is that window right
period. Okay, I'm going to draw another
picture and this will be on the order of
days. So this will be on the order of
days, three or four days up to could be
90 days, could be three months or so.
Okay. Now because you have then very
accurately the absolute magnitude of the
luminosity, then you act you you can get
the distance. So this this allows
seafoods seafoods are allow us to
secrets to
photo distances. So if we find an object
in it object a galaxy or a cluster or
something it has a seafood in it once it
has a seafood in it you can then use
that to say okay we know how far away
that galaxy is we know how far away that
that cluster is so because of this we
use seafs to estimate far away distance
all right so let me get in and the
reason is is okay so I'm going to show
show you the chart the chart that we use
chart looks like this. All right, here
we go guys.
So vertical
line, horizontal line, horizontal line
is the pulsation period [Music]
[Music]
So again, it's this they're timing this
out. I said two days, five days, 8 days,
28 days, whatever.
Okay? And this is nonlinear. So 1 3
3 10
10
30 100, you know, so forth. And
then the average luminosity. So I write
luminosity and there's two lines. It's
actually breaks down and there's I I'll
explain. So draw a line like that and
then a line like that and this will be
about 10 2 and this will be about 10 3
and up here will be about 10 4 times the
luminosity of our sun. So it's L of the
sun. So our son is one on that. So these
two lines go by the following names.
This is the type one seafood line and
that's a type
two seafood line.
Okay. So as I said we clock the
pulsation period and then if we know
what type the sephid is what we just go
to this line and then go over and we
know the magnitude of the absolute
period and
knowing if it's a type
one or two. And I'll explain how we know that
that we
we then
luminosity. Remember, once you know the
luminosity, that's the, you know, the
absolute magnitude. That's the big M.
You know the little M because you
measure just the amount of light that
reaches Earth. You dump that into the
distance magnitude formula that we
talked about last time and then you know
very accurately how far away that
seafood is and then hence the seafood's
embedded in a a galaxy or something you
know how far away that galaxy is. So
let's talk about type
so last page here
guys. So let's
see. So you have to look at the spectra
of the seafid and and you have to look
and see if there's is there metals in
the spectra or is there no metals and
that's how it breaks down. So type [Music]
[Music]
one what we'll see is we'll see a lot of
metals in the spectra. So the spectra
Type
two see if it's and when you look at the
spectra they almost see no metal lines.
pore. Okay. So you have to so while
they're doing the the timing on the pulsation
pulsation
period, there's another group then
that'll do the spectral analysis on the
light. They'll break it down and they'll
say, "Are there any metallic atoms, you
know, that are producing the spectral
lines?" If there are, it's type one. And
then you're on this. So, if you go back
metals. And then the type two, no
metals. And if we go back to the
luminosity versus period chart for the
seafoods. So this is where the seaf
fits and they're the only one that does
this that has this distinct pulsation
pattern where you can measure it and
luminosity.
Okay. All right guys, we'll end there
and we'll uh pick it up next time.
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