Tag Archives: neutron star

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)

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Gravity 7: Recipe for Destruction (Making Black Holes)

by Shane L. Larson

Black holes emit no light, by definition. For many years, the only hope astronomers had of detecting these enigmatic objects was to look for how they interact with other astrophysical objects, like stars and gas. Astronomers have been around the block a few times — they’ve studied a lot of stars, and seen a lot of gas in the Cosmos. What should they be looking for that would clue them in when the stuff they can see has drifted near a black hole? What do black holes do to things that fall under the influence of their gravity?

1280px-Black_hole_consuming_star

If you’ve ever heard about or read about black holes, you’ve learned that their gravity can be strong — extremely strong. This leads to a somewhat deceptive notion that black holes are like little Hoovers, running all over the Universe sucking things up.  The reality is that a black hole’s gravity is strong and can have a profound effect on the Cosmos around it, but only up close.

To get a handle on this, it is useful to go back to the way we first started thinking about gravity — in terms of a field. In the field picture, the strength of gravity — what you feel — is given by the density of field lines in your vicinity; gravity is stronger when you are surrounded by more field lines. There are two ways to increase the strength of the gravitational field.

The easiest way to make gravity stronger is to have more mass. Mass is the source of gravity; when we were drawing gravitational fields, the number of field lines we drew depended on the mass of the object.  The Sun is much more massive than the Earth, so we draw many more field lines to represent its gravitational field.

Two observers (Stick Picard, top; Stick Spock, bottom) are the same distance from objects. For the person near the smaller object, they feel weaker gravity (evidenced by fewer field lines around them).

Two observers (Stick Picard, top; Stick Spock, bottom) are the same distance from objects. For the person near the smaller object, they feel weaker gravity (evidenced by fewer field lines around them).

Another way to increase the strength of gravity is to make an object more compact. You can see this by considering two stars of equal mass, but one smaller than the other. How do their gravitational fields compare? Far from either star, the gravitational fields look identical. There is no way to distinguish between the two based on simple experiments, like measuring orbits. But suppose you were down near the surface of each star. Here we notice something interesting. Both stars have the same number of field lines, because they have the same mass. But down near the surface of the smaller, more compact star the lines are much closer together. This was the signature of gravity being stronger.

Imagine two stars with exactly the same mass, but one is larger in size (top) than the other (bottom). Observers far from either star (Stick Spock, both panels) feel the same gravity if they are the same distance away. For close-in observers (Stick Geordi, both panels) the gravity is stronger. But for the compact star (bottom) the observer can get closer, and when they do, they feel even stronger gravitational forces. The gravity is much stronger near a compact object.

Imagine two stars with exactly the same mass, but one is larger in size (top) than the other (bottom). Observers far from either star (Stick Spock, both panels) feel the same gravity if they are the same distance away. For close-in observers (Stick Geordi, both panels) the gravity is stronger. But for the compact star (bottom) the observer can get closer, and when they do, they feel even stronger gravitational forces. The gravity is much stronger near a compact object.

The field picture of gravity is associated with the idea of forces (it is a “force field”), which is the foundation of Newton’s approach to gravity. But one of the requirements of general relativity when it was developed was that it correctly describe situations where we would normally use Newtonian gravity, as well as any situation that required relativistic thinking. We’ve seen in these examples that gravity gets stronger if an object is more massive, or if it is more compact. In the language of general relativity, we would say “there is stronger curvature” in both these cases. Remember our mantra: “mass tells spacetime how to curve.” Spacetime is told to curve more where the masses are bigger, or when the mass is very compact.

So what does this tell us about black holes? It says that to make an object whose gravity is so strong that the escape speed is the speed of light, I can do one of two things: I can dramatically increase the mass, or I can make the object more compact.  This is the first clue we have to where black holes might come from — they have to be either very massive, or extremely small. We actually encounter both in the Cosmos, as we shall see, but for the moment let’s focus on the small ones. So how do you make things extremely small?

Wrap a balloon in aluminum foil. The foil is like the stuff of the star; the balloon is nuclear fusion, keeping the star from collapsing.

Wrap a balloon in aluminum foil. The foil is like the stuff of the star; the balloon is an outward force, keeping the star from collapsing.

Let’s do an experiment to think about this. Go find a balloon and some aluminum foil. Blow the balloon up (it doesn’t have to be huge) and wrap it in aluminum foil.  This is a mental model of a star at any given moment in its life. Gravity is always trying to pull everything toward the center. But the star is not collapsing — why not?  Deep in the cores of stars, the temperature and pressure is so high that nuclear fusion occurs — through a series of interactions with all the nuclei that are packed together, hydrogen is “burned” into helium. This process releases energy — it’s nuclear fusion power! In your balloon and foil model, the foil is stuff in the star — all the churning roiling gas and plasma that make up the body of a star. What is keeping it from collapsing? In this case it is the balloon, pushing the foil outward — the balloon is acting like the fusion energy bursting out from the core, supporting the star and keeping gravity from collapsing it.

Gravity (turquoise arrows) is constantly trying to pull the star inward on itself. The pressure from the nuclear fusion generating energy in the core presses outward (yellow arrows) preventing the star from collapsing.

Gravity (turquoise arrows) is constantly trying to pull the star inward on itself. The pressure from the nuclear fusion generating energy in the core presses outward (yellow arrows) preventing the star from collapsing.

As a star ages, the fusion process in its core evolves, slowly burning the core fuels into heavier and heavier elements, until a large core of iron builds up. There are no effective nuclear reactions that can sustain the burning of iron into heavier elements.  The iron is effectively ash (that’s what astronomers call it!) and it settles down into the core.  The iron is not burning, so there is no fusion energy pushing outward against gravity’s desire to collapse the core — what’s stopping it?

In addition to the iron nuclei, the core is also full of the other constituents that make up atoms, electrons.  Electrons are a particular kind of particle we encounter in the Cosmos called a fermion. Fermion’s are okay to hang out together, provided they all think they are different from one another (in the language of the physicists — the fermions all have to have different “quantum numbers”); this is a well known physical effect known as the Pauli Exclusion Principle. If you do pack fermions together they dislike it immensely. They start to think they are all looking the same, and they press back; this is called “degeneracy pressure”, and it is what keeps gravity from being able to crush the iron core of the star.

When fusion stops (pop the balloon), there is nothing in the star pushing outward against gravity, so the star can collapse.

When gravity overcomes the electron degeneracy pressure in the iron core (pop the balloon), there is nothing pushing outward against gravity, so the core can collapse.

High above, the star continues to burn, raining more and more iron ash down on the core. The mass of the core grows, and the gravity grows with it. When enough iron amasses in the core, the gravity will grow so strong not even the degeneracy pressure of the electrons can oppose it. When that happens, gravity suddenly finds that there is nothing preventing it from pulling everything down, and the iron core collapses.  In your model, this is equivalent to popping your balloon — you’re left with a lot of material that is not being supported at all, so it collapses.  Collapse the foil shell in your hands — you are playing the role of gravity, crushing the material of the star down into a smaller and smaller space.

When the collapse occurs, the iron nuclei are the victims. The compression of the iron core squeezes down on the iron nuclei, disintegrating them into their constituent protons and neutrons. The extreme pressure forces protons and electrons to combine to become more neutrons (a process creatively called “neutronization”). In less than a quarter of a second, the collapse squeezes the core down to the size of a small city and converts more than a solar mass worth of atoms into neutrons. We call this skeleton a neutron star.

Gravity wants to compress all the matter, to pull down as close together as it can get. The explosion helps gravity move toward its goal by applying astronomical pressures from the outside, squeezing and squeezing the matter down. What stops it?

You hands act like gravity to crush the foil into a small remnant of its former self. There is a minimum crushing size, because the foil presses back against your efforts.

You hands act like gravity to crush the foil into a small remnant of its former self. There is a minimum crushing size, because the foil presses back against your efforts.

Let’s go back to your model. The balloon has been popped — that’s gravity overcoming the supporting pressure of the electrons. The foil has collapsed — that is gravity pulling as hard as it can to get all the material down into the center. Now squeeze that lump of foil as hard as you can; make the smallest, most compact ball of foil you can. Odds are there is some minimum size you can make that ball of foil. What is keeping you from squeezing the foil smaller? The foil itself is getting in the way! It is pushing back against the force that is trying to crush it — you — and you are not strong enough to overcome it!

This is the case with the neutron star. When neutrons are so closely packed together, their interactions are dominated by the strong nuclear force, which is enormously repulsive at very short distances. As more and more neutrons are packed into a smaller and smaller space, they become intensely aware of one another and the pressure from the strong nuclear force grows until it is strong enough to oppose gravity once again.  The collapse stops, suddenly.

The iron core is heavy (more than a solar mass) and moving fast (between 10-20% the speed of light) — it is not easy to stop so suddenly. When the center of the core stops, the outer layers of the core are unaware of what lies ahead. In the astrophysical equivalent of a chain-reaction traffic pile-up, the layers crash down on one another; the outer layers rebound outward.  This rebounding crashes into the innermost layers of the star above the core, setting up a shock wave that propagates outward through the star.  The wave begins to tear the star apart from the inside.

The Western Veil Nebula (NGC 6960), just off the wing of the constellation Cygnus. Visible in amateur telescopes, it is one of the most exquisite supernova remnants in the sky. [Wikimedia Commons]

The Western Veil Nebula (NGC 6960), just off the wing of the constellation Cygnus. Visible in amateur telescopes, it is one of the most exquisite supernova remnants in the sky. [Wikimedia Commons]

Energized by an enormous flux of neutrinos produced by the newly birthed neutron star, the shock is driven upward through the star, until it emerges through the surface, destroying the star in a titanic explosion known as a supernova.  It is an explosion that would make Jerry Bruckheimer proud — the energy released is enormous, for a time making the exploding star brighter than all the other stars in the galaxy combined. The material of the star is blown outward to become a supernova remnant, a vast web of ejected gas and atoms thrown out into the Universe. We see many, many supernova remnants in the galaxy — every one of them is unique, they are all exquisite and beautiful in ways that only the Cosmos can create.

Left behind, slowly settling down into a well-behaved stellar skeleton, is the neutron star.  At the surface of the neutron star, the gravity is enormous — about 200 billion time stronger than the gravity at the surface of the Earth. The escape speed is 64 percent the speed of light. If you fell just 1 millimeter, you would be travelling at 61,000 meters per second (136,400 miles per hour!) when you hit the surface!

Lego Neil deGrasse Tyson and Lego Me visit the surface of a neutron star. [click to enlarge]

Lego Neil deGrasse Tyson and Lego Me visit the surface of a neutron star. [click to enlarge]

But this is still not the extreme gravity of a black hole. If a star is massive enough, the crushing force of the collapsing star and the ensuing explosion is so strong it cannot be stopped even by the protestations of the neutrons. In fact, the infalling matter crushes the matter so strongly that gravity becomes triumphant — it crushes and crushes without bound. The strength of gravity — the warp of space and time — soars. At some point the escape speed at the surface of the crushing matter reaches the speed of light — the point of no return has been reached, but the matter keeps falling right past the event horizon, continuing to fall inward under the inexorable pull of gravity. All the matter is crushed into the smallest volume you can imagine, into the singularity, at the center of the empty space we call the black hole. No force known to physics today is strong enough to overcome this event.

Different effects in astrophysical systems fight against gravity's inexorable pull. If the gravity gets strong enough, nothing can prevent the collapse to a black hole.

Different effects in astrophysical systems fight against gravity’s inexorable pull. If the gravity gets strong enough, nothing can prevent the collapse to a black hole.

The process just described is known as core-collapse and is just one way that astronomers think black holes might be made. Similar explosive events that lead to collapse include the collision of two neutron stars, the parasitic destruction of a small star by a compact companion that grows its mass large enough to collapse, and possibly even the collision of smaller black holes to make larger black holes.

So how compressed do you have to be to become a black hole? The answer for a perfect ball of matter is called “the Schwarzschild radius.” If you squeeze an object down to a ball that fits inside the Schwarzschild radius (that is, it fits inside the event horizon) then no known force can stop gravity from collapsing that object into a black hole. For the Sun, the Schwarzschild radius is about 3 kilometers — if you shrink the Sun down into a ball just 6 kilometers in diameter, the size of a small city, it will be a black hole. For the Earth, the Schwarzschild radius is about 1 centimeter — if you shrink the Earth down to the size of a marble, it will be a black hole.

What it would take to make the Sun or the Earth into a black hole. The Sun as a black hole would cover your town, but you could carry the Earth in your pocket (though this is NOT recommended).

What it would take to make the Sun or the Earth into a black hole. The Sun as a black hole would cover your town, but you could carry the Earth in your pocket (though this is NOT recommended).

Given a notion of how black holes form, astronomers can start probing the Universe, peering into places that should give birth to black holes. The same physical effects that we used to understand their formation can be used to understand how they interact with the Cosmos around them, giving astronomers clues about how to detect them. Next time, we’ll use this information to find out how black holes influence the Universe around them, and use that information to go black hole hunting in the Cosmos.

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This post is part of an ongoing series written for the General Relativity Centennial, celebrating 100 years of gravity (1915-2015).  You can find the first post in the series, with links to the successive posts in this series here: http://wp.me/p19G0g-ru.

[9 March 2015] This is revised version of the original post. I owe many thanks to my colleague, Christian Ott, who pointed out that my original explanation of core-collapse was seriously flawed, following very old (and wrong!) ideas about how stars die. In this revision, I have endeavoured to present a correct but still clear picture of what is going on. Any inaccuracies that still persist are my own.