Why Cepheids Pulsate

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Why Cepheids Pulsate

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In the last video we learned that there are
a class of stars called Cepheid variables.
And these are these super-giant stars,
as much as thirty thousand times as bright as the sun,
with a mass as much as twenty times the mass of the sun.
And what's neat about them is
one, because they're so large and so bright
you can see them really, really far away.
And what's even neater about them is
that they're variable, that they pulsate.
And because their pulsations are related to their actual luminosity,
you know, if you see a Cepheid variable star in some distant galaxy,
you know what it's luminosity actually is
if you were kind of at the star.
Because you can see its period of pulsation.
And so if you know its actual luminosity
and then you know, obviously, its apparent luminosity,
you know how much it's gotten dim.
And the more dim it's gotten from it's actual state,
you know the farther away it is.
So that's the actual value of them.
What I want to do in this video
is to try to explain why they're variable,
why they pulsate.
And to do that, what we're going to think about is
doubly and singly ionized heliums.
And just to review helium.
So neutral helium (let me draw neutral helium) . . .
Neutral helium's got two protons.
It's got two protons,
two neutrons,
and then two electrons.
And obviously this is not drawn to scale.
So this is neutral helium, right over here.
Now, if you singly ionize helium, you knock off one of these electrons.
And these type of things happen in stars.
When you have a lot of heat, easier to ionize things.
So singly ionized helium will look like this.
It'll have the same nucleus,
two protons, two neutrons,
one of the electrons get knocked off, so now you only have one electron.
And now you have a net positive charge.
So here (let me do this in a different color)
this helium now has a net charge.
We could write "1+" here, but if you just write a "+"
you implicitly mean a positive charge of one.
Now, you can also doubly ionize helium if the environment is hot enough.
And doubly ionizing helium is essentially knocking off both of the electrons.
So then it's really just a helium nucleus.
Like this. This right here is doubly ionized helium.
Now, I just said, in order to do this,
you have to have a hotter environment.
There has to be a hotter environment in order to knock off both.
This electron really doesn't want to leave.
I mean, to take an electron off of something
that's already positive is difficult.
So you have to have a lot of,
really pressure and temperature.
This is cooler.
Now, this is all relative.
We're talking about the insides of stars.
So, you know, this is a hotter part of the star vs. a cooler part of the star,
I guess is the way to think about it.
This is still a very hot environment
by our traditional, "everyday" standards.
Now, the other thing about the doubly ionized helium
is that it is more opaque,
which means it doesn't allow light to go through it;
it actually absorbs light.
It is more opaque. It absorbs light.
Or another way, it absorbs that light energy,
that energy will make it even hotter.
So that's just something to think about.
Now, the singly ionized helium is more transparent.
It allows the light to pass through it,
so it doesn't get heated as much by photons
that are kind of going near it,
or through it, or whatever.
It allows them to go through it.
Here, the photons are going to actually heat up the ion.
So let's think about how this might cause a Cepheid variable
to pulsate.
So assuming that Cepheid variables have a large enough quantity
of these ions, we can imagine
that when a Cepheid variable is dim
(So let me draw a dim Cepheid variable.
So I'll draw this in a dim color. So this is a dim Cepheid variable right here.)
In it's dim state, just like this,
you have a lot of the doubly ionized helium.
You have a lot of doubly ionized helium in the star,
or at least kind of the outer surface of the star.
Doubly ionized helium.
And so this does not allow a lot of light to pass through.
So this is the dim part of the pulsation of the Cepheid variable.
Now, because this doubly ionized helium is opaque,
it is absorbing the light.
It is getting heated.
It is getting heated.
And because it's getting heated, it'll cause the star to expand.
So because it's getting heated, it'll become more energetic
and the star will actually expand.
The star will actually expand.
Now, as the star expands because this doubly ionized helium is getting heated,
what's going to happen?
The further away you are from the core of the star, the cooler it gets.
So this expanded because it was getting heated.
But then because it expanded,
the outer layers of the star become cooler.
And since they're cooler, helium won't be doubly ionized anyomre.
Each helium atom can now get an electron from the plasma, I guess we could say,
to become singly ionized helium.
So now, we have singly ionized helium.
We have singly ionized helium.
And now the star is going to be more transparent,
it's going to allow more light to pass through it.
So now this is the bright part of the pulsation.
It's going to allow more light through, so now the star is bright.
But what's happening now?
Because the light is no longer --
or it's not being absorbed as well by the helium
as when it was a doubly ionized helium,
now it's letting most of the light, or a lot more of the light, get through,
it's not going to get heated as much.
And so it won't have the kinetic energy to kind of
keep pushing out, to keep moving outward,
and so it'll collapse back into the star.
And so that this will cool down and collapse back in.
And when it collapses back in, what's going to happen?
When it collapses back in,
when these helium atoms get closer to the center of the star,
to the core of the star,
they're going to be heated again, because they're closer now to the core.
And when they get heated
they're going to become doubly ionized,
so that we have doubly ionized helium again.
And then the cycle will go again:
It is now opaque; it will now absorb more energy;
that will cause it to have more kinetic energy to expand;
once it expands it'll get cool again, and transparent, and bright.
So this is the current best theory of why
Cepheid variable stars are vaiable to begin with.
It's this whole notion of having the doubly ionized helium
vs. the singly ionized helium
in kind of the outer layers of the star itself.