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Lecture 13 A105 Death of Low Mass Stars | Brian Woodahl | YouTubeToText
YouTube Transcript: Lecture 13 A105 Death of Low Mass Stars
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This content explains the life cycle of low-mass stars, detailing their death process, the formation of white dwarfs, and the phenomenon of novae in binary systems.
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All right, guys. Let's begin. We're
going to continue our discussion. And
so, we're going to go ahead and title
stars. And the way that the stars die is
and we break it uh along if it's a low
mass star versus the high mass star. So
mass
less than 8 times the mass of our sun.
So um obviously our sun is considered a
low mass
star. And
then we have the way that the high mass stars
die. And these
sun. Okay.
So we'll uh focus first on the way the
low mass stars die. So let's do a bullet
here entitled this low
low
mass stars and and then next lecture
we'll do the high mass stars. So how
they die. Okay.
So, so recall that we have the helium
core fusion occurring
um and we're producing the carbon and oxygen
form of mostly
photons. Then the question is, well, are
you ever going to get to a point where
you can start
to fuse the carbon and the oxygen that's
building up in the core? And the answer
is in a low mass star, you can't.
least 600 million
temperature. And you know just to remind
ourselves you know hydrogen is only 10
million. I say only only 10 million
but so hydrogen's 10 million and then
helium is 100 million but then to go
ahead and begin to work on the you know
you're going to need least 600 million
Kelvin. So, let's just put in here
And you're just not not going to get
that 600 million in the low mass star.
star.
Kelvin. Okay.
oxygen. Okay. So, we're we've got
a core of helium that's at 100 million
Kelvin. It's fusing. It's producing um
the carbon and oxygen. And so,
eventually you're going to run out of
the helium. And so you're building up
that core of inert carbon and oxygen.
And as you start to run out of the
helium, you're going to see a drop off
in the in the fusion rate. So you're
going to start to see a drop off in the
And so if you don't make those uh
photons then you don't have a countering
agent to the compressive forces of
gravity. So gravity then is going to begin
begin
[Music]
And the inner regions of the star uh
And so what happens is you begin to heat
up a thin uh spherical shell of helium
uh above that inert core of the carbon
and oxygen. And so you can then get that
thin helium shell to 100 million Kelvin.
And so it'll begin
um helium
fusion
begins. And just a reminder then above
that shell you're going to have that
hydrogen shell that's you know it's
picture. And uh, of course, I don't have
So, okay. So, there's an inert core.
Oh, let me move this up.
up. Inert
Inert
core of
oxygen. And then above that right
there is a helium shell that's hot
enough and it's undergoing fusion. So
it's producing uh more carbon and oxygen
and then dumping it on that core. So
this is where we have the helium
helium
shell fusion.
So it's fusing the hydrogen to produce
helium that gets dumped on that helium
shell right below it. So you kind of see
this layer process. And then of course
helium. And the word inert remember
means we're not at a temperature that
that material can undergo nuclear
fusion. So we use the word
inert. So inert
helium. Okay. So that's kind of our
picture. Now when I go back to what my
language I have here. So I'm going to
just go back to my page two.
Um so we now have this
um helium shell fusion and so the photon
pressure is significant and it's going
to push the outer regions out farther
and farther away to larger
radiuses and this then forms what we
call an AGB star the which means asmtoic
giant branch star. So let's write fill
helium [Music]
shell
fusion. So that's
this shell right
here. This one that's right above that inert
inert
Okay, this
this forms
forms
a run out of room here. So, I'm going to
go back below my drawing
now as a asintoic giant
And so asic giant branch star
uh which we call an AGB
AGB
star. So there's a reason why. So let me
go to that drawing. Let's go to our HR
diagram and and show you what's
happening here.
And again, I think I can squeeze it in
here. I hope I can. Uh, so what we want
to do is we want to do an HR. So we're
going to
do absolute magnitude or luminosity
vertical and then of course surface
temperature along
the the bottom here as
always or the color, whatever you want
to call
Okay. So, I'm just going
to throw on the main sequence line. I'll
just throw that in
there. Okay. And then we look at a star
here. So, you know, we're uh main
sequence. And now, here's the path that
you got to sketch in. So, there's a path
that looks like this. Then, put a point
there. And then it walks back this way.
And then put a turning point there. And
here.
Okay. So, it walks this way, turning
point there, walks back that way,
turning point here, walks up this way.
So, we got to
label these three little paths. Okay.
So, from here up to
here, we have what we discussed earlier,
shell
fusion. Okay. Then this turning point is
when you have the helium flash in the core.
And then this path
here you now it's hot enough in that
helium core that that helium core is now
fusion and eventually you exhaust all
the helium
uh in the core. And so the core helium fusion
fusion
ends and gravity then go
has a head and
compresses and then you so you get
that hot enough on that thin helium
shell just above the core and then you
get the helium shell fusion and that's
this path and along that path. That's
what we mean. That's That's an AGB star
when it's along this path.
helium shell
shell
AGB. And then I'm going to put some uh
words below this,
but put a little star and then this. And
flash. Okay. So we're this AGB is when
you track along this path right here. We
got this is this path and then this path
and now this path and this is when we're AGB.
AGB.
Okay. So I'm going to scroll up here and
go on to the next
page. Page
four. So at the end of AGB right up
occurs and possibly more than once. So
it's kind of a you know boom
um helium shell flash
does so this causes so let me let me
expand.
And anytime you have a material and it
you expand it, it cools. So to to cause
cool. And because it cools
uh the uh electrons and the
ions um nuclei
um of the hydrogen helium will combine
because it's cooled. Then it's now you
you no longer have you're above that
ionization temperature. So this causes
the outer layers to expand and cool.
Thus that that means you you're going
from the plasma phase back into the gas
phase. So this causes the outer layers
recombination. And when you have re
combination, you produce photons. So you
photons. So we have these two mechanisms
that are producing quite a bit of
photons. So we have the helium shell flashes.
So, [Music]
[Music] helium
photons. And these are so both of these
are photons and it blasts away the outer
stars. And that that material getting
blasted away is what we call planetary nebula.
So what happens now is on the HR diagram
the star
uh moves
And the reason it moves leftward is
you're getting the higher temperature
because you're exposing the hot cores
blasting away the cooler outer material.
So you're going to move left leftward on
your HR diagram. Remember these are the
hot surface temperatures here, cool
surface temperatures over here. So
you're going to move leftward and you
move downward because you no longer have
a a significant fusion. So you're not
producing the light. So wrapping around,
you know, we're going to end up right in
this little band. And if we go back to
the earlier lectures, that's the land of
dwarfs.
So new page here.
here.
Five. Let's just put a bullet here.
dwarf. Okay. So, let me explain the verb
uh the words there. So white meaning,
you know, something's white hot. So it's
very hot. That's where the word white
comes. And all you have left is that
just that core of the of the carbon and
the oxygen. So you have a just a small
leftover remnant of the original star.
And so that's what you know small that's
where the word dwarf comes
from. Now in a white dwarf, there's no
nuclear fusion. And remember to fuse
either the carbon and the oxygen you
have a minimum you need 600 million
Kelvin. You're you're not even close to
that there. So you have no fusion. So
you have a very dense structure though,
very crystallin dense structure of the
carbon oxygen. So you have tremendous
gravity. So gravity compresses that. And
then you say, well, wait a minute.
What's going to halt the gravity from
fully compressing that? And there is a
mechanism. We're going to talk about
that, but right now I want to tell you
white dwarfs are stable objects.
Remember that in in general in the star
there's these these two competing
forces. The outward push of the photon
pressure which is a byproduct of nuclear
fusion and the compressive effects of
gravity wanting to compress the star. So
in general, gravity is always
balanced from further contraction due to
the outward flow of those photons.
That's the photon pressure. It's not the
case in the white dwarf. The white
dwarf, you don't have the temperature
required to go ahead and fuse the carbon
and oxygen. So gravity compresses, but
there is a repulsive agent that comes
into play. And that repulsive agent is
electron degeneracy pressure. So, we're
pressure and then we're going to discuss
this and
uh this is a byproduct of uh quantum
physics. Okay. So first off, let me say white
dwarfs are so looking back at white
dwarfs are stable against gravity even
though there is no fusion.
um of a white dwarf. And so, the way
that we draw it is you just draw a circle.
And of course the circle itself is inert
carbon and
oxygen. So over here on the left side
inside the circle right inert
inert
carbon and
oxygen. Okay. And of course we have the
effects of gravity. These are supposed
to be
arrows that want to further compress
that structure. So, we'll put some
arrows going inward like this and just
label those
gravity. But then countering
pressure. And I'm not going to be able
to fit the words in here.
So I'm just going to do it like that.
And this is our little picture of a white
dwarf. Okay. So that's kind of that
these arrows that point outward are the
byproduct of electron degeneracy pressure.
pressure.
And these two forces gravity and
electron degeneracy pressure are in
perfect balance. And then so that size
that white dwarf is stable. It stabilizes.
stabilizes.
Okay. So, let me explain and what's the
details here. So, I'm going to scroll up
ionized. And what that means is then
those electrons are stripped away from
the nuclei from the nucleuses of the
carbon and oxygen. So the carbon and
oxygen are
nuclei and
electrons are
separated. That's what we mean by ionization.
Um the nuclei are then squeezed into a crystallin
crystallin
arrangement. So the carbon nucleuses and
the oxygen nucleuses. So
arrangement and then the electrons are distributed.
nuclei
Okay. So the important thing is these
electrons. So electrons
um do not like to be next to one
another. They're what we call firmians. So,
So, but
but [Music]
[Music]
not like to
to
be next to each
each
other. And if you've taken a chemistry
course, this is often called the
principle. So, gravity is trying to
squeeze together these electrons and get
them right next to each other. But the
um electrons each want to maintain a
unique set of quantum numbers. And so
what begins to happen is each
electron. So the lowest energy electron
fills in that low energy level. And then
to satisfy the unique quantum numbers,
the next electron has to have a
different set of quantum numbers. And so
the energy quantum number has to be
slightly greater for that one. And that
means that electron is vibrating more
quickly than the lower energy one. And
then the third one is even vibrating
more than the second one. And so these
electrons each one goes to higher and
higher vibrational motion. And that then
maintains the unique set of quantum
them must uh
faster and I'll just say so
unique. Well, this continued, you know,
ladder of increasing vibrational
energy that produces this balance push
back against gravity because this is
what we call kinetic pressure and that's
So
against gravity and that's the picture
that we were discussing earlier.
So gravity wants to squeeze them
together, but the electrons are
vibrating quicker and quicker so that
each one has a unique set of quantum
numbers. And that vibrational motion
then is what we call kinetic pressure.
It's like photon pressure. It pushes
back against the gravity. And then
that's what sets the size of the white
dwarf. And that's why the white dwarf is
a stable object. It's no longer contracting.
So the question is is this electron?
So maybe just this this thing that I've
just described here that's the electron degeneracy
pressure which I I don't know I started
anyway so the question then becomes is
this electron degeneracy pressure
unlimited? is is it always able to push
back against
gravity? And the answer is no. So that
gets us to our next
So in
1940 the Indian uh phys uh physicist uh
uh found
that as
dwarf
has a mass
mass less
less than
than
1.4 times the mass of our sun, the
electron degeneracy pressure can balance
gravity. But of course, if it has a mass
greater than 1.4 times the mass of our
sun, no. Then the electron degeneracy
pressure can't.
So found that as long as a white dwarf
has a mass less than 1.4 times the mass
of the
gravity. So if you think about this
statement, this puts an upper limit on
the mass of a of a white dwarf. And that
upper limit is in honor of Chandra
Secar. That's what we call the Chandra
Seekar limit. So, I don't know. Let's
put a star here and title this
this Chandra
mass
is 1.4 times the mass of our
sun. That's the Chandra Sakar limit in
honor of Chandra
Sakar. Okay.
So our sun is going to end up as a white
dwarf. So I don't know I'm on the page
end
dwarf. White
dwarfs are very dense.
Remember density is mass divided by
volume and the the Greek letter is row.
So the density of a white
dwarf is
about 1 * 10^ the 9
kilogram per cubic meter. So a
billion kilograms per cubic
meter. Okay. So let me put that
in a perspective that something that a
matter will
weigh five
tons. So you have a teaspoon of white
dwarf matter on earth you weigh it
weighs five tons. That gives you kind of
a a perspective of what we mean by 10
the 9 kg per cubic meter. All
nova.
Nova. So remember we were saying that
when you look up at the stars in the
nighttime sky, a majority of them are binaries.
binaries.
two stars that are in uh orbit around a
a central mass center mass point.
They're very close together and they're
orbiting around that center mass point.
Um that's a binary. So now I'm going to
there's a certain type of binary and
that's called a nova. And so we can um
discuss that.
binary
with a main sequence star and a white
A nova
happens if
if
the So remember we
use mph s for main sequence. So if the main
main sequence
sequence star
star is
is inside
inside
the it's a technical word I'll explain
limit explain it here in a
bit. So let's see page nine. Um,
And the forces of gravity then on on the
white dwarf compress that
thin hydrogen that's been sucked off of
the main sequence and it compresses it.
It heats it up above 10 million Kelvin
and you get fusion. So and depositive on
on the white
dwarf. Um and as temp
reaches 10 million Kelvin and that's
because the gravity of the white dwarf
will go ahead and compress that
hydrogen. So it reaches 10 million
million
Kelvin you get
photons and this is this blast then of
nova.
Okay. Now Rocha limit. So let
me let me draw a picture and then our
last bullet will be the explaining the
Rocher limit because once you have the picture
picture
uh then it's much easier to
explain. So we're going to draw the
picture. So it goes like this. So we got
to have a white dwarf. So draw a circle
there. And this is the white dwarf.
I'll see if I can shoehorn in white
dwarf. I maybe should have made that a
little bigger that
circle. Okay. And then it's a binary. So
somewhere else we have a main sequence.
sequence. Remember the main sequence.
We're on the main sequence line. You
have the hydrogen in the core that's fusing.
fusing.
Okay? And then right about
here, I want you to put a dash
line like that. And this dash line is
limit
and what and I'm going to explain the
Rocher limit here below it.
Basically in a nutshell in the Rocher
limit here if I look at I've got some
matter here that belongs to the main
sequence. But here's the
problem. Matter that's right here.
There's two t there's two forces that
well there's a bunch of forces but the
two main forces the competing forces are
as following. There's the self-gravity
of the main sequence and then there's
the gravitational force of the white dwarf.
dwarf.
So any material that's on the left side
of the Rocher
limit means that the gravity force of
the white dwarf for this material is
stronger than the self-gravity of the
main sequence. And so what happens is it
pulls it off of the main sequence and
pulls it
onto the white dwarf. And then that thin
little shell of hydrogen gets spread out
around the white dwarf. And the forces
of gravity then compress it, heats the
temperature up above the 10 million
Kelvin and you get that
that
fusion and that that boom that blast is
then the
nova. Okay. So the material getting suck
It's simply the product that the main
sequence got too close to the white
dwarf such that the gravity of the white
dwarf is now stronger than the
self-gravity of the main sequence. And
so that the main sequence can't hold the
hydrogen material anymore. And all the
material that's inside this dash line
will get pulled off onto the white
dwarf. So last bullet is the roche limit.
gravity another
gravity this is where sorry white dors
And that means then that the hydrogen's
going to get sucked
off of the
uh main
sequence and deposited on to the white
dwarf and gets compressed gets above 10
million Kelvin. Boom. uh nuclear fusion
of that hydrogen. All right, guys. We'll
stop there for today and pick up next time.
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