What Happens in an Expanding Star’s Core?

Depending on their mass, stars can remain stable for millions and even billions of years. The most massive stars live for “only” about 10 million years, but models predict that the least massive live for much longer—longer than cosmologists believe the universe has existed.

As long as stars are stable, they exist on the “main sequence.” That’s just a fancy word for the best balance between temperature and mass. For a while now, we’ve been exploring the main sequence in depth, and I’ve shown you how stars eventually lose stability and “leave” the main sequence.

As stars exhaust their fuel, their internal structures change drastically. Their cores contract, but their outer layers are forced to expand, and they become giants. You’d think the next thing we’d cover would be what happens to these giant stars, right?

Well…not quite! At this point, something downright weird is going on in their cores, and it’s well worth a closer look…

First, remember what’s going on inside the star. Right now, all of the hydrogen in the star’s core has been fused, leaving behind helium “ashes” that can’t be converted to energy.

Until the core began to contract, pressures elsewhere in the star weren’t high enough to ignite hydrogen fusion.

But now, it’s time to recall a process that also happened, ironically, as the star was just beginning to form. When a giant molecular cloud begins to contract—the first stage of star formation—it is able to form a star because the gravitational energy from contraction is converted to thermal energy.

Wait, what the heck are gravitational energy and thermal energy, again?

Thermal energy is the total energy of all the moving particles in an object. Basically, the faster all the particles are moving, the hotter something is. And the slower the particles are moving, the cooler the object is.

Thermal energy is different from kinetic energy, which is simply the energy of movement. If all the particles in an object—say, a molecular cloud collapsing to form a star, or the helium ashes in the core of a giant star—are moving in the same direction, then they each have kinetic energy, but they must all be moving randomly to have thermal energy.

Gravitational energy is a kind of kinetic energy. Like kinetic energy, it is energy of movement, and particles have it when they are all moving in the same direction. Specifically, though, gravitational energy is the energy particles have when they are falling toward a center of gravity.

In a giant molecular cloud, the center of gravity is where the star begins to form, and in the core of a star, the center of gravity is…well, you guessed it. The very center.

The core is contracting. That means it has gravitational energy. But its helium nuclei simply can’t fall forever—it’s against the laws of physics. They have a finite distance to travel. Once they reach the center, they begin to collide with one another, and as a result, they begin to bounce around randomly.

Now the star’s core has thermal energy.

This thermal energy ignites a thin spherical layer or “shell” of hydrogen fusion just around the core. As I described in my last post, this shell burns outward through the star like a brushfire and dumps its helium ashes into the core.

Now, the core has no choice now but to contract under its own weight. It is completely inert. There are no nuclear reactions producing energy. It has thermal energy from the collisions of helium nuclei, but it is not managing to fuse them because the pressure just isn’t high enough.

Between that, and new helium nuclei getting dumped into the core as the hydrogen fusion shell burns, the core is gaining mass but not producing enough energy to balance that mass. And so it contracts…and contracts…and contracts.

That’s when weird things start happening.

The core is now ridiculously tiny. If it were the size of a baseball, the outer envelope of the star would be about the size of a baseball stadium.

(It is, of course, much larger, because we’re talking about stars—but that’s how small it is in comparison to the rest of the star.) But it still contains roughly 12% of the star’s mass.

That may not sound like much, but for an object that has contracted from a much larger size, that is an absolutely crazy density—somewhere around 1,000,000g/cm3. On Earth, a teaspoon of this material would weigh as much as a large truck.

I know. Crazy, right?

At these kind of crazy densities, gas stops obeying the usual laws of physics. Normally, the pressure of a gas depends on its temperature. The hotter the gas, the higher the pressure. But that’s not the case here.

Instead, it’s time to take a dive into some quantum mechanics.

Quantum mechanics, in case you don’t know, is the science of how the smallest stuff behaves. So far on this blog, I’ve introduced you to atoms—the building blocks of the universe—and the particles of atoms, namely protons, neutrons, and electrons.

When talking about the insides of stars, we deal with atomic nuclei, which is the central mass of protons and neutrons, and free-floating electrons—that is, electrons that are not in orbit of an atomic nucleus.

Quantum mechanics dives deeper into the realm of ultra-tiny stuff than we need to right now. It covers the behaviors of quarks, neutrinos, positrons, and a number of other tiny particles. For now, though, we only need concern ourselves with two laws of quantum mechanics.

The first law makes sense if you think about the behavior of electrons inside an atom. Electrons occupy specific energy levels, which you can think of as a bit like the rungs of a ladder.

Just as a person can stand only on the rungs of a ladder and not on the space between the rungs, electrons can only have specific amounts of energy. In order to gain more energy, they have to jump at least all the way up to the next rung of the ladder. They can’t exist in the middle—in between energy levels.

In chemistry, spectroscopy, and other sciences that deal in discovering what stuff in the universe is made of, we look at the energy levels electrons occupy within an atom.

But within stars, the same law works for free-floating electrons. Even though they are not orbiting an atomic nucleus, they are still restricted to having specific amounts of energy.

The other law of quantum physics that we care about right now is the Pauli exclusion principle, which states that two identical electrons cannot have the same location and occupy the same energy level.

Wait…what the heck does that mean?

Well, let’s take this apart. What does it mean for electrons to be identical?

That one’s easy—they have to be spinning in the same direction.

Yeah, okay, I know, that still doesn’t make much sense. Why do they spin? How the heck does spinning in the same direction make them identical?

I hate to break it to you, but…I don’t know what the heck is going on here. Quantum mechanics is a strange world where all the physical laws we know and love just seem to break down for the heck of it.

What I do know is that electrons can only spin one of two ways. If they’re spinning in the same direction, they’re identical. If they’re spinning in opposite directions, they’re not—and they can occupy the same energy level.

So what does this mean for the core of a star?

Simply put…it means that ladder I mentioned earlier gets filled up.

In a normal gas, and in the core of any star that’s fusing nuclei on the main sequence, there’s plenty of room for electrons to move around. They can have their choice of energy levels.

In degenerate matter, though—the stuff that exists in the inert helium core of a giant star, where helium nuclei can’t fuse—the material is packed so densely that the Pauli exclusion principle kicks in.

Suddenly electrons no longer have a choice of energy level. They must occupy an energy level—that is, have a specific amount of energy—that’s not already taken by another electron spinning in the same direction.

I know, weird. Quantum mechanics is.

These electrons are effectively locked into their energies, which correspond directly to their speed of motion (yes, kinetic energy still applies). They can’t slow down because there are no open lower energy levels to drop into.

And they can’t speed up unless they get a huge energy boost, enough to jump clear out of the degenerate electron matter and into the unoccupied energy levels above.

This means that it’s still possible for the electrons to break free of their degenerate state. But it’s really, really hard. Like, ridiculously hard. Believe it or not, degenerate matter is harder to compress than the toughest of hardened steel.

Here’s the crazy thing, though. It still counts as a gas, because states of matter are defined only by the thermal energy of their particles. And degenerate matter has a crap ton of energy. It’s just…degenerate.

But…wait a sec. What about the nuclei? Have we forgotten about them?

Nope—they’re another part of the crazy quantum physics equation!

The electrons in the core control its pressure, simply because there’s a lot more of them. We’re talking helium here, and helium atoms come with two electrons. So for every helium nucleus, there’s two free-floating electrons in this degenerate soup.

The nuclei, however, control the temperature of the gas. This is because the temperature depends on the thermal energy of all the particles, and the nuclei don’t have to obey the Pauli exclusion principle.

They can move however the heck they want, and have any amount of energy. They don’t have specific energy levels at all.

That means that while the pressure of degenerate gas is next to impossible to change, the temperature can be driven up easily. And so as the envelope of a giant star expands, the core contracts to a point where it stops…because its electrons just can’t fit any closer together.

What happens next for the star? What are the consequences of a degenerate core? We’ll explore these answers coming up.

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