Stars might seem like the most stable of objects, always shining bright in the same patch of sky night after night, but they too will come to end one day. This applies even to our own Sun, whose own fiery end in a few billion years’ time may consume the Earth. After a star’s final throes there is normally a final ember, present and visible, but far from the former brilliance of the star, commonly found nestled at the centre of a stellar nursery. These star remnants are collectively known as degenerate stars.
Degenerate stars come in several different forms, but here we’re taking the moral high ground and sticking to the astronomical kind. The bit of Physics key to understanding these special kinds of stars is called degeneracy pressure, and it comes from two important parts of quantum mechanics.
Firstly, there is the Pauli exclusion principle, which states that no two particles can occupy the same state. Then there is the Heisenberg uncertainty principle, which is a bit more complicated and is a classic example of quantum mechanics being really weird. This states that there is a limit to what can be known about a particle. This limit is fundamental and absolute; it does not come from measurement problems. It is simply impossible to know exactly where a particle is and know how fast its moving at the same time. In fact, the more you pin down exactly where a particle is at any given moment, the less you can know about its speed.
These two principles combine as matter becomes extremely closely packed. As the particles are forced closer they run up against the exclusion principle, which gives a well known position as the particles cannot overlap. As the uncertainty in the position is low, the uncertainty principle dictates the uncertainty in speed must be high. This means that the particles are moving fast, which generates an outward pressure, in exactly the same way hot air molecules in a tire move faster and can cause tire blowouts.
When stars run out of Hydrogen to fuse they can explode exceptionally violently in supernovae, or as the Sun will, expand into Red Giants. These will also eventually burn through all their Helium, however they are too small and light for the subsequent gravitational collapse to generate enough heat to begin Carbon fusion. Without nuclear fusion there is nothing to prevent the collapse, until the star runs up against degeneracy pressure from electrons. This is a White Dwarf star, likely to be the ultimate fate of our Sun.
With temperatures of around five times the Sun and enormous pressure, the conditions are sufficient for nuclear fusion of Hydrogen, but there is no Hydrogen present as it was used in earlier fusion processes. White Dwarves are typically made up of Carbon and Oxygen, the products of those earlier fusion processes, but the pressure is large enough to compress the star into a single vast diamond. Despite having a mass comparable to the Sun, White Dwarves have a radius of only around 10,000 km, comparable to the Earth, which makes them incredibly dense. In fact, a single teaspoon of a White Dwarf would weigh 5 tons.
If a star is 8-25 times as massive as the Sun, its collapse will not be stopped by the electron degeneracy pressure. Instead the collapse will continue until it runs up against degeneracy pressure from neutrons, which can be much more densely packed than electrons. Much more.
Neutron stars have all the mass of a typical star like the Sun, but are only 7-20 km across, about the same as a city, so the one pictured has a mass about 750,000 times that of the Earth. The surface temperature is about 1000 times that of the Sun and the density is frankly ridiculous. A single teaspoon of a neutron star weighs about as much as all the cars on Earth put together. Something dropped from a metre about the surface would hit the surface going at over 6 million kph, such is the gravitational strength. Because of the immense compression, Neutron stars are also the most perfect spheres in existence. On the whole, it’s fair to say they’d win most categories in a stellar top trumps set.
But even White Dwarves and Neutron stars don’t last forever. They will slowly cool over millennia, becoming black dwarves (none of which are yet thought to exist because the Universe hasn’t been around long enough for the cooling to finish), before evaporating away into the cosmic dark. Of course, you might be wondering what happens when a star is so incredibly massive that it overcomes even the neutron degeneracy pressure when it collapses. The answer is even more astounding than the Neutron star.