Tag Archives: degeneracy pressure

Black Holes 3: Making black holes from ordinary stuff

by Shane L. Larson

If you are exploring the Cosmos, and either by design or accident, find yourself plunging toward a black hole, on a beeline that takes you directly across the horizon, you don’t encounter anything along the way; all you feel is the inexorable pull of gravity pulling you farther and farther down. When you reach the event horizon, the nominal “surface” of the black hole, what do you encounter? 

Nothing.

The event horizon is simply the invisible line in space where gravity has become so strong that even if you were travelling at the speed of light, you could not escape; the event horizon is a boundary that once crossed, Nature says you are never coming back out — the inside of the black hole and only the inside of the black hole is in your future. That’s a big statement, but you cross this point in space without even an alarm to let you know you are trapped. It’s as easy as walking across a line drawn in the sand at the beach.

A black hole with the MASS of the Sun is not even close to the SIZE of the Sun! Here the approximate size of a solar mass black hole is shown near the city of Evanston, IL — only about 6 kilometers (4 miles) across. What is it made of? Nothing tangible — it is empty space, filled with nothing except gravity itself! [Map: Google; Image: S. Larson]

Through the horizon and as you fall inward you still encounter absolutely nothing. This has previously led us to ask, “What is the black hole made of?” Based on what you experience, we had concluded “a black hole is made of pure gravity.” But gravity, as we learned early on in our thinking about the world, is a consequence of mass (or energy if you take the modern understanding of mass and energy being related). That normally would imply that the black hole was made of mass of some sort, but as our gedanken experiments have paradoxically shown us, there is no mass to be encountered when travelling toward and into black holes! 

A thoughtful cosmic explorer (or astronomer) would take that bit of confusing information and ask a very pointed question: “how do you make a black hole, then?” The motivation for such a question is built out of our common experience. If you want to make something, whether it is a gallon of dandelion wine, a guitar, or a cinnamon roll, you take other things and transform them into the new thing.  So what are the other things that can be transformed into a black hole? And how do you change them from being ordinary things into pure gravity? Those are very good questions, and to be honest with you here at the beginning, we don’t know all the answers. We only know part of the story, the penultimate explanation for how it happens. Some of the story is still unknown, and lies beyond the boundaries of what we currently understand about the Cosmos. That is part of what astronomers and physicists investigate and attempt to understand every day.

Astronomers have seen many phenomena in the Universe that are explained by black holes. The question is where do they come from? [Image: Wikimedia Commons]

How do we start? Where ever you are, look around you and pick up the nearest thing you can see. Maybe it’s a rock, a bagel, a book, a Lego brick, your cat — whatever. Here I’ve picked up a fountain pen. Why does the fountain pen, or any other object, have form? What is it that makes it a solid tangible object? If you try to squeeze the fountain pen, it may deform slightly, but generally resists any effort to squeeze it out of shape. Why? Because as you press the fountain pen, the building blocks of which it is made, the molecules and atoms, fight to hold their shape. They press against their neighboring atoms, and when the pressure from your fingers tries to force them closer together, they press back against you in tandem, resisting your attempt to move them.

If you press hard enough, you can sometimes squeeze them together or change how they sit next to each other. Sometimes you are stronger than a material and break the object. Some objects are hard to compress, but they can certainly be deformed if you apply a force to them in specific ways. It’s hard to flatten a paperclip into something like a piece of foil, but it is not too difficult to bend it back and forth into a new shape. Ultimately what you can do physically to any object depends on how the building blocks of its structure respond to forces applied from the outside.

(L) Very solid objects, no matter how hard I squeeze them, retain their shape. The atoms that they are made of resist external forces. (R) Some objects can be deformed, bent, or broken, like these paperclips — their atoms resist some external forces, and yield to others. [Images: S. Larson]

Now consider a slightly different example. Go to your kitchen and find a party balloon in your junk drawer. Blow it up and tie it off so it is maybe 20 centimeters across. Take a couple of sheets of aluminum foil, and wrap the balloon up. What happens when you try to squeeze the foiled balloon? It deforms a little bit under the force of your hands, but when you let go the pressure from inside the balloon pushes it back into its round shape.

A balloon wrapped in foil as a heuristic model of a star. The balloon presses outward against the pressure from your hands that is trying to collapse the foil.

This simple balloon and foil model is completely analogous to a star. The foil is playing the role of the outer layers of the star that we see when looking through our telescopes (the “atmosphere” or the upper layers of the star). Your hands pressing down are like gravity, trying to pull everything that makes up the star into the center. Opposing the inward press of your hands, the balloon represents something inside the star pressing outward against the pull of gravity. We know the outward press is the energy released by nuclear fusion deep in the core of the star. This balanced state, where the inward pull of gravity is precisely counterbalanced by the outward push from the energy created by fusion, maintains the round and stable size and shape of the star. Astronomers call this state hydrostatic equilibrium.

When the balloon is popped, nothing prevents your hands from collapsing the foil. This is similar to fusion ending in the core of a star — nothing presses outward, and gravity collapses the star.

Now, gently hold the foiled balloon in the palm of your hand and have a friend pop the balloon with a needle. The support from the balloon vanishes, leaving you holding an unsupported shell of the foil. You are gravity, so squeeze the foil down. It should be easy — there is nothing to fight back against you. You can, and should, squeeze the foil down into a small, aluminum ball. Ball it up, and squeeze it into the smallest ball you can. Once you’ve squeezed it as hard as you can, stand on it trying to squeeze it smaller. If a member of your family is stronger than you, ask them to squeeze it even smaller.

How small did you make it? Can you make it any smaller? The answer is “probably not.” Why? Because all of the aluminum atoms in the foil are resisting being pressed together, far stronger than you can press them together with your hands or feet. This is not dissimilar to the fountain pen we discussed above — all the atoms that make up the aluminum are pressing out, resisting being pushed any closer together than they already are.

The exact same thing happens in Nature. Gravity takes collections of stuff — stars, planets, anything round — and tries to pull it together as strongly as it can. Eventually everything gets crowded together, and through a variety of interactions resists the inward pull of gravity. For stars in the middle of their lives, they exist in hydrostatic equilibrium, with the inward tug of gravity balanced against the outward push from the fusion in the core.

Squeeze the foil as hard as your possibly can. Eventually your strength will be matched, and the ball will get no smaller.

When a star reaches the end of its life, the fusion in the core shuts down. That moment is like you popping your balloon — the star suddenly finds itself without much outward pressure at all, and the inward pull of gravity takes over — the star collapses. The collapse is the beginning of a supernova explosion. 

For our interests here we are not interested in what gets blown out, but what happens in the innermost core. There, the titanic pressures of the collapse and explosion break apart the atoms, and breaks apart the nuclei of the atoms. You may recall from school that atoms themselves are made of smaller bits — the smallest bits are called electrons which orbit around a nucleus made up of bits called neutrons and protons. Like you standing on a wine glass, the inward force of gravity during the collapse crushes every atom, breaking every one apart into these shards called electrons, protons, and neutrons.

In the soup of protons and electrons and neutrons that results, the protons and electrons are forced together and turn into a neutron plus a small particle called a neutrino. This conversion process is called “neutronization” (really — sounds like something from a superhero movie, right?) — the conversion of most of the matter of the core into neutrons. 

A neutron star (diameter 20 km) scaled to the Chicago skyline. [Image: LIGO-Virgo/Nick Gertonson/Daniel Schwen/Northwestern]

This core that remains is called a neutron star when it settles down, and its gravity is extreme beyond belief.  It has about 1.5 times the amount of stuff in as the Sun, but squeezed down into something about 20 kilometers across — the size of a city.  At the surface, the gravity is 200 BILLION time stronger than the gravity you are experiencing right now on Earth. What are the consequences of such extreme gravity? Imagine you could take a walk on a neutron star (and you could certainly NOT walk, but go with me here) and you had the unimaginable misfortune of encountering a cliff only ONE MILLIMETER high. What would happen if you fell off? On a neutron star, falling off a one millimeter high cliff means when you reach the bottom you will be travelling about 227,000 kilometers per hour (141,000 miles per hour)!

The gravity of a neutron star is extreme, but a neutron star, like its parent star, maintains its shape as a round, spherical object — it is in hydrostatic equilibrium! Gravity is trying to press down, but something just as strong is pressing back. In this case, it is the neutrons that make up the star. Neutrons do not like to be near each other and push back when they are squeezed into small spaces — this is called “neutron degeneracy pressure” (for the quantum mechanics aficionados among you, this is a consequence of the “Pauli exclusion principle”). The reason gravity could not collapse the neutron star is because the neutron degeneracy pressure is enough to stop it.

But there is a funny truth about gravity. All four of the fundamental forces of Nature have a range of distances over which they act, and their strength varies over those distances. They also each affect only certain kinds of objects in the Cosmos. Gravity, however, is completely indiscriminate — it acts on and affects everything that has mass and energy, which as it turns out is everything in the Cosmos!

The consequence of that simple fact is if you make a big pile of anything, gravity always tries to pull it closer together, and will succeed in pulling it together until it is opposed by a stronger force (for example the hydrostatic equilibrium, and the neutron degeneracy pressure examples we noted above).

We only know the masses of a few neutron stars, most between the mass of the Sun, and two times the mass of the Sun. Can heavier ones exist in Nature, or do they all turn into black holes? Explore the stellar graveyard on your own with this interactive tool at CIERA. [Image: Frank Elavsky/Northwestern University]

Most of the neutron stars we have observed in the Cosmos up to now have masses between about 1.4 times the mass of our Sun, up to around 2 times the mass of our Sun. Why aren’t their bigger ones? We certainly see huge stars, up to 30 or 40 times the mass of the Sun — when they explode, they definitely have larger cores that should leave behind bigger remnants, bigger stellar skeletons. So can a neutron star bigger than the ones we’ve found in the Cosmos exist? You can imagine taking one of the known neutron stars, and slowly piling more and more mass onto it. Each jelly-bean or rock or bit of starstuff you drop on the neutron star increases its mass, which increases its gravity, which makes gravity pull inward more strongly. Eventually, gravity will get so strong that the neutrons cannot resist any more — gravity overwhelms the degeneracy pressure, and presses the neutrons closer together. 

Concentrating all the mass of neutrons together makes gravity even stronger, which pulls all the mass of the neutron star even closer in a never-ending cycle of just making gravity stronger. At this point, there is no known force in the Universe that is stronger than gravity. Nothing can oppose gravity’s inexorable inward pull, and everything that was a neutron star gets smaller, and smaller, and smaller, until the gravity is so strong that not even light can escape. We have a name for that.

A black hole.

So at last, we arrive at the answer to our question: we make black holes by squeezing matter together. Black holes are not stuff but they are made of stuff in the beginning. 

Where is all that stuff now? It is concentrated somewhere behind the event horizon, where we cannot see. Mathematically, the laws of gravity suggest it is concentrated into an infinitely dense point called a singularity. It is… … … something. Something that completely defies our understanding of the Laws of Nature, and is the subject of much consternation and study on the part of modern physics and astronomy researchers.

Now we are curious creatures, and it is completely natural to ask “what is inside the black hole?” or “what is inside the event horizon?” The answer quite pointedly is you can NEVER know unless you jump in yourself! The emphasis really is on the word UNLESS — nothing prevents you from jumping in and looking around; the only prohibition is on your ability to come back out to visit your friends who watched you jump in. The prohibition that the speed of light is the ultimate speed limit in the Cosmos, coupled with having to travel faster than the speed of light to get out of the event horizon, means you will never hear about anything that happens on the “inside” of a black hole second hand!

But we can use our mathematical understanding of gravity to predict what you would experience if you jumped in, and the predictions are weird and disconcerting. We’ll talk about some of that gravitational weirdness next time. 

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This post is the third in a series about black holes.

Black Holes 01: Imaging the Shadow of Darkness

Black Holes 02: What are black holes made of?

Black Holes 03: Making black holes from ordinary stuff (this post)