﻿ Matter and Neutron Stars

# Stuff

 Matter has a lot of space in it. The currently understood model of an atom comprises a nucleus (made up of a cluster of protons and neutrons), which is surrounded a number of electrons.
 Early in our school lives we’re taught to think of these electrons in orbits, spinning around like planets, but as we learn more, this model is updated to describe the electrons as a nebulous cloud. The shape of this cloud is defined as a probability density function which describes where electrons are more, or less, likely to be at any time (in the event we could even measure them without perturbing them!) What’s not often comprehended, however, is just how much ‘nothing’ there is in an atom.
 To help appreciate just how much nothing, let's rescale things. If we took the nucleus of an atom of, say, Gold (shown left), which has a nuclear radius of approx 7.3x10-15m, and scaled it up to the size of basketball (0.12m), how far away would the furthest electron be? As the electrons could be anywhere in their clouds without defined edges, the concept of atomic radius is a little involved, but an accepted atomic radius for a Gold atom is 1.3x10-10m (distance to the outermost electron).

Scaling this atomic radius to basketball scale, puts the furthest electron approx 2.1 km away from the basketball! (about 1.3 miles) That’s an awful lot of nothing in-between! You probably can’t even see a basketball 2.1 km away with the naked eye. That really is a lot of nothing!

Everything you touch, see, sit-on, hit, walk into, stub your toe on, throw, or eat is actually 99.9999999999999% nothing (yes, that really is thirteen nines in the decimal!)

Stuff is 99.9999999999999% nothing!

OK, when we get down to this quantum level, what is ‘stuff’ and what is ‘nothing’ start to have weird and undefined concepts, the point I wanted to make is that when something appears ‘solid’, it’s really a macroscopic concept and the fact that you don’t fall through the floor is not because stuff is in the way and unyielding, it’s because of the quantum interaction of the particles, and the Pauli exclusion principle that prohibits electrons having the same state. Particles are keeping themselves apart from each other with sufficient force to make matter ‘rigid’ even though just about everything in there is space.

### Removing that Space

 What would happen if we removed the intra-atomic space? What if we could push atom nuclei together closer than the electrons typically allow? The result would be material that is found in a Neutron Star.

Neutron stars are created when a star a few times the mass of our Sun runs out of fuel. The outward pressure generated by fusion reduces rapidly, allowing gravity to pull the star in on itself and trigger a supernova, where the outer layers of a star’s atmosphere get blown into space.

The remaining matter continues to collapse under gravity, forcing electrons and protons to be squashed together and become neutrons, and then squashing all the neutrons together. The neutron star will have less mass than its parent star (usually about 1.5 times the mass of the Sun), but this mass will be confined by gravity to a region of just 20 kilometres (12 miles) across!, leading to an incredibly, incredibly dense object.

It's almost impossible to comprehend how dense these stars are. A mass greater than our Sun compressed into a sphere with a diameter of just a couple of miles. To attempt to show this to scale, here's a map of Seattle, with a neutron star to approximate scale.

That little sphere just to the East of Seattle contains more mass than one and a half times the Sun. Below you can see a depiction of the scale of the Sun to the Earth. It's almost impossible to even make out the Earth without zooming in. Neutron stars are really dense.

Image: Windows to the Universe

### Neutron Stars

There are so many superlatives associated with Neutron Stars. Here are a few:

• A teaspoon full of neutron star would have a mass of about a billion tons.

• Gravity on a neutron star is a couple of billion times stronger than gravity on Earth. It is strong enough to bend radiation (gravity lensing); astronomers can see behind them!

• The power from the supernova that birthed it gives the star an extremely quick rotation, causing it to spin several times in a second. Neutron stars can spin as fast as 43,000 times per minute, gradually slowing over time.

• Some neutron stars have jets of materials streaming out of them at nearly the speed of light. As these beams pan past Earth, they flash like the sweep of a lighthouse beam. This pulsing appearance led them to be called pulsars.

### Quark Stars

So are neutron stars the densist stars in the universe? Maybe not. There is theory that even denser stars may be around called Quark Stars. These are comprised of even more dense material, Quark-Gluon Plasma, in which the quarks are deconfined.

It's not yet fully understood, in fact, just how dense neutron and quark stars really are. Theory suggests that the neutrons in the center of a neutron star could be closer together, by orders of magnitude, than the neutrons in a 'regular' atomic core.

### Other massive things

 So what about Black Holes, I thought they were massive and pulled things in, even light (which is why they are black). What's the relationship between Black Holes and Neutron stars? How are black holes formed? Are they more massive? Are they more dense? I thought black holes were formed in just the same way you just described a neutron star is formed? What gives? Well, It all depends on the initial mass of the donor star …

### switch(mass) {case:SMALL white_dwarf(); break; … }

 Like some giant astronomical case statement, what happens when a star dies depends on its mass. Stars are giant fusion reactors. Starting with Hydrogen, under intense pressure and heat, atoms are fused to make heavier elements. Hydrogen is fused into Helium, then as stars get older, other heavier elements are fused and formed. Nothing last forever, however, and eventually a star runs out of fuel to 'burn'. What happens next depends on the mass of the material left in the star. Whilst a star is burning, the heat in the star pushes out and balances the force of gravity. When the star's fuel is spent, and it stops burning, there is no heat left to counteract the force of gravity. Whatever material is left over collapses in on itself. How much mass the star had when it dies determines what it becomes. Stars about the same size as the Sun become white dwarfs, which glow from left over heat. Stars that have about three times the mass of the Sun compact into neutron stars. And a star with mass greater than three times the Sun's gets crushed into a single point, which we call a black hole.
• A white dwarf is also incredibly dense, (a million times denser than gold, for instance, but it's another million times order of magnitude to get the density of a neutron star). In a white dwarf, the degeneracy pressure between electrons (that is, the Pauli exclusion principle as applied to electrons) is sufficient to balance gravity, and we just get a lump of slowly cooling dense matter.

• The gravitation forces of dying star with a higher mass, as we have seen, compresses the matter sufficiently until the degeneracy pressure between neutrons (that is, the Pauli exclusion principle as applied to neutrons) is sufficient to balance gravity, and we get a neutron star.*

• In a more massive dying star yet, the gravitational forces are so strong that all matter collapses to a single point (called a singularity), and it is this singularity that is the heart of a black hole.

*Also, I understand, there's a good chance that neutron stars, given enough time, will also turn into black holes. As the material in a neutron star gets so compressed, it passes something called the Tolman–Oppenheimer–Volkoff limit; the neutrons have become compressed so much after the neutron degeneracy pressure have failed to hold up the star.

### Black Holes

A singularity is a one-dimensional point with a huge mass, and no volume. As the eminent American physicist Kip Thorne describes it, it is "the point where all laws of physics break down". The exact secrets of what happens there may, forever, be a mystery because, even if a probe could be sent, whilst we could communicate to it, there is no way to receive any signal broadcast from it.

Black holes are 'black' because the pull of gravity from their enclosed singularity is so strong that not even light can escape. They have an edge, called an event horizon, inside of which, light can't escape. (The gravitiational pull of the singularity being so strong that the escape velocity needed would exceed the speed of light; an impossibility).

The event horizon is why black holes have shape. A black hole, initially, doesn't have any more mass than the star that formed it, and so as to its 'density', it really depends on the volume that you consider this mass is distributed over. At the singularity, by mathematical definition, it's infinitely dense, but if you consider a black hole to be what you see enclosed by the event horizon, then it's less dense than a neutron star, on average.

You can't actually 'see' a black hole, nor the event horizon, but gas, dust, and stellar debris is attracted towards it, like debris circling the drain in a bathtub. This spinning debris is called an accretion disk. With the strong forces applied to the debris, and the speeds at which this disk revolves, and the heat it generates, produce powerful high energy radiation emissions (X-rays and Gamma-rays). These accretion disks are also known as quasars (quasi-stellar radio sources), and are some of the oldest known parts of the universe.

Black holes are not monsters that will eat the rest of the universe. Sure, if you pass over the event horizon you will not be able to escape, but outside of this, a black hole behaves just like a massive object and celestial mechanics apply between it and other bodies in just the same way as they would for a non black hole. If our Sun were replaced/turned into a black hole of the same mass, the Earth would not be sucked in; it would orbit just the same way. (There would, however, be many more differnet issues to worry about if that happened!)

### XKCD

No article about supernovae and neutron stars would be complete without a couple of refences to Randall's work.

If you want to compare the energy released by a neutron star creating supernova to an atom bomb exploding next to your eyeball, then look further than here.

If you want to want to find out what would happen "If a bullet with the density of a neutron star were fired from a handgun (ignoring the how) at the Earth's surface, would the Earth be destroyed?", then you'll have to buy and read his excellend book What If?: Serious Scientific Answers to Absurd Hypothetical Questions.

Randall's book is a great read. Buy two; one for yourself, and one as a present for your best nerd friend.

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