Above is a theoretical rendering of a white dwarf, the collapsed husk of a low-mass or medium-mass star. Interestingly enough, these strange cosmic objects—which begin their existence as intensely hot balls of carbon the size of the Earth—may eventually cool off and crystalize into giant space diamonds.

White dwarfs are made up of free-floating hydrogen and helium nuclei and degenerate electrons—and their mass is supported by the nature of these electrons.

But degenerate electrons, like any other material, have a specific material strength. What happens if they’ve, well…just got too much stuff to support?

At this point—the Chandrasekhar limit of 1.4 M_☉ (solar masses)—a white dwarf must collapse. No white dwarf can be more massive than 1.4 M_☉.

Let’s quickly review where we are in following the process of a massive star’s evolution.

We’ve seen the star exhaust its fuel until it’s left with a core of inert iron. Unlike any other element, the iron nucleus can’t be fused or split for energy, so that’s the end of the line for a massive star. Having stopped generating enough energy to support its own weight, the star begins to collapse.

Then, a shockwave blows most of its interior and atmosphere apart in a supernova explosion, which leaves behind a supernova remnant…like the Crab Nebula.

The supernova remnant is made up of most of the interior and atmosphere of the star. What’s left behind is the iron core, still in collapse but too massive to reach stability as a white dwarf. And that’s where the good ol’ laws of quantum mechanics come into play.

Remember electron spin from my post on the degenerate core of a medium-mass star? I was talking about stars of less mass then, but the same quantum mechanics applies.

Essentially, electrons can spin in one of two ways, and if two are spinning in the same direction, they’re identical. If they’re spinning in different directions, they’re not.

The Pauli exclusion principle says that no two identical electrons can occupy the same space and have the same amount of energy. Because electrons can only have specific energies, like rungs on a ladder, this means we can get to a point where they’re as squeezed as tightly together as they can get.

In this diagram, the red balls represent electrons and the lines represent specific energies they can have. The matter on the right is degenerate because the electrons are packed together as closely as they can get…and still be electrons.

But…what does that mean?

The collapse of a star’s core is a violent process that produces loads of high-energy photons. Gamma rays, in particular, break apart the atomic nuclei (protons and neutrons) that are floating within this degenerate electron soup.

The result: protons from the nuclei are now free to combine with electrons and actually become neutrons.

I know. Quantum mechanics is weird.

From a strictly mathematical standpoint, though, this makes sense. Protons have a positive electric charge; electrons are negatively charged. It makes sense that if you stuck them together, the charges would cancel out and result in neutrally charged neutrons.

So…is the core stable now?

As it turns out, neutrons actually follow the Pauli exclusion principle, too. Why? Because—surprise surprise—they spin in ways analogous to electrons. Which…doesn’t make a whole lot of sense to me, but then again, that’s quantum mechanics for ya.

Anyway, here’s the key. Since neutrons obey the Pauli exclusion principle, they must also behave in the same ways as degenerate electrons. As in, they have material strength. But their material strength is greater than that of degenerate electrons.

Which means they have the material strength to support a collapsing star’s core of more than 1.4 M_☉.

Crazy, right?

So, we know from the behavior of neutrons—and from the fact that degenerate electrons can’t support more than 1.4 M_☉—that there should be stellar remnants out there that are made of a degenerate neutron soup. But…exactly which stars should meet this end?

As we covered in a previous post, even massive stars that begin their lives with enough mass to exceed the Chandrasekhar limit can lose a great deal of mass to their superwind. They can lose enough mass to eventually meet the same fate as their medium-mass siblings.

However, this only applies for stars between 8 and 10 M_☉; more massive stars can’t lose enough mass in their lifetime to change their explosive fate. So, stars more massive than about 10 M_☉ should become neutron stars.

But even degenerate neutrons can’t stand up against the collapse of stars more massive than about 20 M_☉. Those stars will contract past the point of neutron soup, until…

Well, I’ll save that for when we actually dive into black holes!

Heh, heh…not literally. That would be very uncomfortable.

Anyway. How much mass, exactly, does that mean the neutron degeneracy pressure can support?

That’s a hard question to answer because we can’t make pure neutron material in a laboratory. Theoretical calculations suggest that neutron stars themselves can’t be more massive than about 3 M_☉. (Which means that the remaining 7-17 M_☉ of star stuff goes into creating the supernova remnant.)

There’s also an upper limit on the size of a neutron star—about 10 km in radius.

Imagine that. A neutron star could fit into a space smaller than Los Angeles.

They’re way denser than Los Angeles, though. Neutron stars have a density of around 10¹⁵ g/cm³—which means that a lump of their material the size of a sugar cube would weigh 500 million tons on Earth.

What else can we theorize about neutron stars?

First, they should be very hot. They have contracted a great deal, so gravitational energy should have been converted to great quantities of thermal energy. And due to their small size, they should cool very slowly because of their exceptionally low luminosities—similar to white dwarfs.

Second, they should spin rapidly, also because they’ve contracted to a ridiculous degree. The same principle holds true for, say, an ice skater—if you draw your arms in close to your body, you spin faster. Similarly, if a star contracts, it spins faster. So neutron stars should be among the fastest-spinning objects of all.

Third, neutron stars should have very powerful magnetic fields. But why?

Stars are made up of ionized gas, and magnetic fields can’t move freely through that (for reasons beyond the scope of this post). So when the star contracts, its magnetic field lines get caught in the gas and forced to squeeze tighter right along with the star…which, by a quirk of magnetism, can make the field up to a billion times stronger.

People, these massive stars started out with magnetic fields more than a thousand times stronger than the sun’s. So…neutron stars should have insanely strong magnetic fields.

So, we’ve now covered a lot of theory about neutron stars. But how do we know that any of it is true?

I’ll cover the evidence we’ve found of neutron stars in my next post!