Now that we’re finally talking about white dwarfs, we’re getting into the really cool stuff.
In my last post, we explored planetary nebulae, and we left off with a question: where does the fast wind that forms planetary nebulae come from? Well, remember that planetary nebulae are formed from the atmospheres of medium-mass stars, but there’s still the stellar interior to worry about.
White dwarfs are objects comparable in size to our own Earth. They are the remains of medium-mass stars like our own sun. Often, you can see a white dwarf at the center of a planetary nebula with a large telescope. Together, they form what’s left of a star after it loses stability completely.
But there’s way more to a white dwarf than that…
First, allow me to introduce you to a white dwarf you may be familiar with: Sirius B, the faint companion to the brightest star in the sky, and also the first white dwarf to be discovered.
See that faint little dot almost hiding in Sirius A’s shine? That’s not a camera artifact. That’s the star’s companion white dwarf, 8000 times fainter than the brighter star.
Yeah. It’s super faint.
Which makes sense, really, when you think about it—if these objects really are comparable in size to Earth, they must be tiny as heck. It’s very hard to see planets that orbit other stars because of how far away they are. The only reason we have a chance at separating Sirius B from its companion star’s glare is because it emits its own light, unlike a planet.
So, where is Sirius B on the H-R diagram?
There it is, toward the hot end of the scale for white dwarfs. It’s actually ridiculously hot as stars go (if you count it as a star). But why?
Well…the answer actually starts with the degenerate matter we talked about a while back. I know, it’s really been a while. Don’t worry, I’ll refresh your memory.
The groundwork for a star to become a white dwarf was laid way back when the star first began to expand into a giant—before even helium began to fuse in its core.
Before helium began to fuse, the core had run out of hydrogen fuel and was collapsing under the weight of the layers above it. That collapse generated thermal energy, which produced radiation pressure, and that’s why the star was expanding to begin with—the outer layers were being pushed outward.
Because we’re talking about white dwarfs, we’re talking specifically about medium-mass stars—stars that can’t immediately fuse helium. Even when they exhaust their hydrogen fuel and the core is heating up under collapse, it’s still not hot enough to ignite helium fusion.
Degenerate matter is what happens when the core collapses so much that the normal laws of physics break down, and quantum mechanics comes into play.
Quantum mechanics are the laws that describe the weird world of subatomic particles. We’re talking about atomic nuclei—specifically helium—and free-floating electrons.
There are two important laws you need to know to understand degenerate matter. One follows from the rules of how electrons orbit atomic nuclei—that they orbit in energy levels. That is, there are specific amounts of energy, like rungs on a ladder, that electrons can have, and they can’t exist between rungs.
The second law is the Pauli exclusion principle, which says that two identical electrons cannot have the same location and occupy the same energy level.
Which means, in plain English—or, as near as I can actually get it to plain English—that two electrons spinning in the same direction can’t be in the same place and have the same amount of energy.
If electrons were, you know, normal particles that behave according to the normal laws of physics that we know and love, this wouldn’t be a problem. After all, energy exists on a spectrum, and the electrons could—in that world—have plenty of differing amounts of energy to go around.
But…it doesn’t work like that, thanks to the idea of energy levels. There aren’t enough energy levels to go around when electrons are squeezed so closely together.
So, in degenerate matter, here’s what happens:
On the left is normal matter, where electrons are free to move about however they please. They’re not squeezed together by the full weight of a star that’s not producing enough energy to support itself.
On the right is degenerate matter, where only two electrons—each with an opposite spin, so they’re not identical, whatever the heck that’s supposed to mean—can occupy each energy level, and they’re all squeezed together. This matter is extremely dense. It’s literally packed as densely as it can get.
In fact…if a lump of degenerate matter the size of a beach ball were transported to Earth, it would weigh as much as an ocean liner.
I know. Crazy, right? That’s the stuff inside a white dwarf.
In my last post, we wondered where the fast wind that compresses the gases of a planetary nebula comes from. The answer: it comes from the intensely hot white dwarf at the center.
White dwarfs are so hot because the collapse of its interior produces thermal energy, and that thermal energy doesn’t go into un-degenerate-ifying the core. It just gets conducted through the material in the core and emitted from the star as radiation.
So here’s the next logical question. The star is no longer producing energy, and it’s emitting radiation, so it has to run out of energy at some point, right?
A white dwarf’s heat can’t last forever. It will eventually cool off. But that energy will last for some time because white dwarfs are very small and, consequently, not very luminous. Remember that luminosity doesn’t just refer to the visible light we see—it also refers to all other forms of energy a star produces.
Essentially, if an object is faint, it’s not losing energy very fast. So it’ll last for a long time.
No white dwarf should be old enough to have cooled off completely yet. But once it does, its carbon-oxygen interior may in fact crystalize to form a giant space diamond. At that point, astronomers would call it a black dwarf because it has become cold and dark.
As for the rest of a white dwarf…not all of its material is degenerate. Most of it is, but the pressure of gravity that forces its material into degeneracy is much lower at the surface. There, ionized helium and hydrogen make up a hot atmosphere.
This atmosphere isn’t very thick, though. Remember how a lump of this degenerate stuff the size of a beach ball would weigh as much as an ocean liner? Well, this whole object is the size of Earth, but has a lot more mass than Earth. Its surface gravity is in fact 100,000 times that of Earth.
The result? A white dwarf’s atmosphere is so thin that if it were on Earth, people on the top floors of skyscrapers would have to wear oxygen masks.
And it gets weirder.
Meet the Chandrasekhar limit, named for the astronomer who discovered it, Subrahmanyan Chandrasekhar.
Mathematical models predict that if you add mass to a white dwarf, it will actually shrink. Why? The added mass increases its gravity and, somehow, squeezes the darn thing even tighter. So…what happens if more mass is added?
The graph above shows that the radius is predicted to shrink to zero, a physical impossibility (until we start talking about black holes).
So…let’s say we have a star whose mass before becoming a white dwarf is equal to the mass of the white dwarf in the models plus the added mass. Theoretically, when the star becomes a white dwarf, it should shrink to a radius of zero.
Which is impossible. It wouldn’t be a white dwarf then.
That suggests that there is actually a mass limit on white dwarfs. Stars over 1.4 M☉ (solar masses) cannot become white dwarfs.
Now, here’s the question of the day. Are these crazy objects really stars?
If you define a star as a sphere of gas that generates energy by nuclear fusion, then…no. A white dwarf is not a star. But we can call it a compact object, a category shared by two other super-cool stellar remnants: neutron stars and black holes.
We will be exploring those very soon!