Hey Crazies.
I’ve been meaning to do a video on white dwarves for a while.
No no no, white dwarf stars!
I did my 90-some-page thesis on them.
It lives on the shelf over here.
They’re one of those weird astronomical objects that can’t be understood
without quantum mechanics.
Let’s start at the beginning.
No no no no, too far back!
I mean where white dwarfs come from.
Stop it!!
There are three types of stellar corpses.
The big stars leave behind black holes and the medium ones leave behind neutron stars.
It’s the small stars that leave behind white dwarfs.
Different low-mass stars live slightly different lives, so they can end up as white dwarfs
made of slightly different things, but it’s always a white dwarf.
The vast majority of active stars in the present universe are low-mass stars.
About 70% of them are faint red dwarfs.
The point is, eventually we're going to have a lot of white dwarfs floating around.
We should probably understand them.
Classically, these things shouldn’t even exist.
Gravity should collapse them into black holes, but we know that doesn’t happen.
We can see some of them through telescopes, so we know they exist.
The problem is balance.
Smaller stuff like these ice cubes don’t collapse under their own gravity because the
bonds and intermolecular forces hold the atoms in place.
You can say the same thing for stuff as big as asteroids or planets.
But stars are different.
They’re so massive, that their self-gravity breaks the matter down.
Molecules and even atoms fall apart and they become a giant ball of plasma.
Stars have something else to keep from collapsing.
Radiation pressure!
As the gravity pulls inward, the fusion in the core releases light and that light exerts
an outward pressure to balance gravity.
It’s what we call “Hydrostatic Equilibrium” because it behaves like a fluid with balanced
forces.
White dwarfs are kind of in-between planets and stars.
They’re a dead star, meaning no more fusion or radiation pressure, but they’re way too
massive for molecules to hold up.
Actually, if white dwarfs are white, then they're emitting light, so there is radiation pressure.
Yes, yes, but not nearly enough.
Remember, radiation pressure depends heavily on momentum and, therefore, energy and ultimately
frequency.
Without fusion, all you get is the standard black-body light, most of which is only in
the visible range.
That’s pretty low energy.
Fusion in an active stellar core releases high-energy gamma rays, which have 10 million
times the energy.
Besides, eventually, even that will bleed out into space.
The white dwarf will get cold and black and it still won’t collapse.
I really need to stop being so depressing.
Anyway, if it’s not intermolecular forces and it’s not radiation pressure, we need
another explanation and it comes from Quantum Mechanics!
Remember from the previous video, how you could only put two electrons into a single
atomic orbital?
We called it the Pauli Exclusion Principle.
That same rule applies here.
It’s just that white dwarf matter isn’t nearly as organized.
Gravity is so strong that molecules get crushed.
The atoms end up overlapping so much that the electrons don’t belong to specific atoms.
They flow through the whole star like it’s one big spherical box.
It’s called “Degenerate Matter” because it’s of a lesser quality.
The quantum states are very simple and a lot of them share the same exact energy.
It’s a mess.
But, because of the Pauli Exclusion Principle, you can’t have all the electrons in
the lowest energy.
There can still only be two in each state, so the rest get forced into a higher and higher
energy states, just like in an atom.
This behavior acts just like an outward pressure.
We call it “Electron Degeneracy Pressure” for obvious reasons and it’s enough to hold
back gravity, up to a limit.
The Chandrasekhar Limit!
Anyway, calculating this limit can be tricky, so we’ll want to be careful.
One!
We don’t need to use General Relativity.
While white dwarf stars are dense, they are neither massive enough nor dense enough to
require us to consider curved space-time.
Trust me.
I’ve done the calculation both ways.
You get the same result.
Two!
We do need to use Special Relativity.
Remember how most these electrons are forced into higher energy states?
Well, they’re also forced into higher momentum states, which means most of them are going:
fast fast!
I’ve also done this calculation both ways.
You don’t get the same result.
Now, what was that last thing?
Oh right!
We just need one more piece of information: The limiting factor.
We need to know what makes the Pauli Exclusion Principle fail.
That’s where the protons come in.
The more massive the white dwarf, the stronger its gravity, so more massive white dwarfs
are actually smaller in size.
Their electrons are confined to a smaller and smaller space, which means they’re moving
faster and faster.
At some upper limit, the electrons are moving so fast that they combine with the protons
to make neutrons.
It becomes a neutron star, which we’re saving for another video.
The upper mass limit for a white dwarf is
is 1.4 times the mass of our Sun with a diameter of only 1083 miles.
Some people describe it as a giant diamond in space, but this density is way passed diamond.
So how many of you to see one these up close?
Let me know in the comments.
Thanks for liking and sharing this video.
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And until next time, remember, it’s OK to be a little crazy.
The featured comment comes from qbslug who asked
Why do atoms seem to be the most stable with p-oribtals?
It's not really about the p-orbitals, it's about the shell as a whole.
The p-oribtal just tends to be on the outside of the shell.
For that atom to gain an electron in a bond
it would have to go up an entire extra energy level.
That's not easy.