There’s a whole bunch of different types of supernovae: Type Ia, Type Ib, Type Ic, and Type II. I am not going to talk about Type Ib and Type Ic because they’re variants of Type II and thus really boring. Type Ia are kind of interesting but the ones I really want to talk about today are Type II supernovae, which are what everyone thinks of as a “classical” supernovae. To make a Type II supernova you take a really, really big star – eight or nine solar masses is the minimum limit – let it chew through its supply of hydrogen through nuclear fusion over a few hundred million years (the bigger a star, the shorter its lifespan) and then wait for the fireworks to start.

Once the star has finished fusing hydrogen into helium, the nuclear fusion process will stop and there will no longer be any outwards radiation pressure resisting the inwards pressure from gravitational collapse. The star will therefore start to gravitationally collapse (duh). This compresses the helium at the heart of the star, heating it up and kickstarting helium fusion into carbon while incidentally restoring some sort of hydrostatic equilibrium to the star, halting the collapse. As helium burns at a higher temperature than hydrogen the core of the star expands and then cools, resulting in a layer of hydrogen surrounding a layer of helium inside which helium is fusing into carbon.

Eventually all the helium runs out and the process repeats; the star begins to collapse, the core compresses, the carbon ignites and the star then expands into a four-layer structure: hydrogen, helium, carbon, and then the inner core where carbon is fusing into neon. This cycle continues again and again – neon goes to oxygen, oxygen goes to silicon, and silicon goes to iron, with a new element layer being added to the star each time giving it this onion-like structure. As the elements being fused get heavier the fusion reaction gets hotter and quicker; it takes a star millions of years to burn its supply of hydrogen, but only a few days to fuse silicon into iron. As a result the star is becoming increasingly unstable, and once the star has fused all of its silicon that instability cumulates as iron fuses into nickel-56, which cannot be further fused as the next step up in the fusion chain – zinc-60 – would actually consume energy to fuse rather than releasing it. The fusion process therefore hits a brick wall. Literally.

Fusion stops. The outer layers of the star now resume their gravitational collapse towards the core unimpeded by any further fusion pressure. What happens next depends on the mass of the core of the star.

Less than 1.38 solar masses: The outer layers of the star accelerate in their collapse until they’re travelling at a sizeable fraction of the speed of light (0.23c). As the star gets smaller the temperature and density of the core increases and the star begins spitting out all sorts of harmful cosmic radiation. Eventually the core has been crushed up so small that what’s propping it up against further collapse is something called the electron degeneracy pressure; this is a quantum thing involving the Pauli exclusion principle¹ which says that no two electrons may occupy the same quantum state. If you think back to your secondary school chemistry you may recall that electrons orbit the atomic nuclei in strictly ordered shells of 2-8-8-8-etc. You can’t fit more than 8 electrons into a shell; you have to start a new one if you want to add more electrons to the atom. The Pauli exclusion principle is roughly analogous to this; it sets a limit on the number of electrons you can cram into a single space by forcing new electrons to occupy the lowest empty energy level rather than sharing one that’s already occupied by another electron. Jam enough electrons together and the “lowest empty” energy level will still require a staggering amount of energy for a new electron to occupy, and if the gravitational force of the star cannot provide this amount of energy the star will halt its collapse. In other words, the Pauli exclusion principle provides a quantum pressure that counteracts the collapse of the star – the electron degeneracy pressure.

Once the collapsing stellar matter hits the electron degeneracy pressure limit (and remember, it’s a crapload of mass travelling at 0.23c) it “bounces” off the core and releases a staggering amount of energy in a supernova explosion. This ejects most of the star’s mass at speeds of up to 0.1c as well as an awful lot of radiation, which is bad news for anyone living within a couple of hundred light years. Supernova release so much energy that they briefly outshine all other objects in the sky; a supernova in a another galaxy will outshine and obscure all the other stars in that galaxy combined. This is where the term nova comes from (new star), as the first we see of a supernova is usually a bright new point of light in the sky where there was none before.

There’s still a remnant of the star left after the supernova explosion: the sub-1.38 solar mass core. This is now compressed up very small into a white dwarf; a dead star with the mass of the Sun but with the diameter of the Earth. White dwarves no longer produce heat or light through fusion – all they emit is leftover thermal radiation from the collapse process.

Between 1.38 and 2 solar masses. As above, except the gravitational force of the collapsing star is now so great that the electron degeneracy pressure can no longer prop it up. The star’s gravity doesn’t exactly break the Pauli exclusion principle but it does sidestep it; while the energy requirements to smoosh up electrons together into ever higher energy levels may still be excessive, there is an out provided in that the energy of the electrons will now be high enough that it becomes possible for them to directly bond with protons, creating a whole mess of neutrons. Instead of a white dwarf, the core remnant is now a neutron star propped up by the neutron degeneracy pressure. Since we’ve gotten rid of all those pesky electrons and protons and are just left with neutrons we can compress the core remnant up much more than we would be able to otherwise; neutron stars are thought to be less than 12km in diameter whilst retaining a mass of up to two Suns, making them incredibly dense and giving them the same comedy tidal properties mentioned in the spaghettification part of Tuesday’s post.

A quirk of neutron stars is that they retain all of the parent core’s angular momentum as they collapse. In other words, you now have the total rotational momentum of a 100,000 kilometre diameter core packed down into a 12 kilometre diameter remnant, making them rotate ridiculously fast; neutron stars spin at anywhere from a few rotations per second to hundreds of rotations per second. Since neutron stars blast out intense beams of electromagnetic radiation from their magnetic poles (which are not necessarily aligned with their rotational poles) this can produce a “lighthouse” effect if you happen to live on a planet which is swept by the beam where your radio telescopes will pick up very strong, very regular radio signals that can be mistaken for alien radio transmissions. In actuality it’s just a specific type of neutron star called a pulsar.

Between 2 and 3 solar masses. The core might create a quark star but nobody has any idea how these work or even if they exist so they’re boring. BORING.

Greater than 4 solar masses. The core’s gravitational force is so great that even the neutron degeneracy pressure can’t prop it up against collapse. At this point conventional physics breaks down, the remnant continues to collapse until it disappears up its own fundament, and a singularity is created, with all the associated hijinks detailed in Tuesday’s post.

What’s so important about a stellar core having 1.38 solar masses? This is something called the Chandrasekhar limit, which is the maximum mass a white dwarf can have before it collapses further into a neutron star. It’s possible for white dwarves to exceed the Chandrasekhar limit after they’ve gone supernova by absorbing mass from another nearby source like a companion star; however, if a specific type of white dwarf (a carbon-oxygen white dwarf) does this it instead heats up and undergoes a runaway reaction as it approaches the limit, resulting in a second supernova. Since the trigger mass for this supernova is the same every time (about 1.38 solar masses) the luminosity of the supernova is the same every time; this is the Type Ia supernova I talked about a couple of months ago that can be used as standard candles.

So now you know how black holes are created. Be sure to bore all your friends with this information the next time you’re at a party!

1. It’s quantum in that we’re trying to jam a bunch of electrons together to the point where we can no longer distinguish between them based on their position, therefore we must be able to distinguish between them based on their energy level.

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Wait no that came out completely wrong. What I was trying to say there was that black holes have this rather exotic reputation amongst the population at large, mainly because various sci-fi films have given them all sorts of weird and wonderful attributes – they’re portals to other universes, they’re mechanisms for time travel, they’re power sources for starships etc. etc. They seem to capture the imagination rather more handily than any other celestial object before or since, and so I thought I’d spend a little bit of time talking about them.

What is a black hole?

It’s an odd little region of space created by a whole bunch of mass scrunched up very small into a single point called a singularity. Gravitational force is inversely proportional to the square of the distance separating you from an object’s centre of mass as per

where G is the gravitational constant, M is the mass of the larger body, m is the mass of the smaller body (usually negligible where massive stellar bodies are concerned) and r is the distance between the two.

Note: it’s been pointed out to me that it’s possibly easier, instead of just chucking the m away because it’s very small, to shift it over to the F side of the equation. Since F = ma it then follows that F/m = a, meaning GM/r^2 = a, or acceleration. If you’re having trouble visualising what I mean when I say “The gravitational force is such-and-such N/kg,” try imagining it in terms of acceleration instead.

Thanks to the r² in that equation the force that a massive body like, say, the Sun exerts on you is usually comparatively small. Even if you went all the way to the surface of the Sun it would still be comparatively small, because the Sun is very big and you’ve still got about 695,000 km between you and the Sun’s centre of mass. Gravitationally speaking the Sun is a bit of a weakling; in terms of its heat and energy throughput you’d be burned to a crisp before you ever got that far, though, so it’s probably wisest not to stow thrones in grass houses.

Now consider the Sun if it were scrunched up into one of these singularities. A singularity outputs no radiation and has no surface to stop infalling objects, so it’s possible for us to get much, much closer to the singularity than we would a regular stellar object. Even though the singularity has a similar amount of mass to the Sun and hence exerts a similar level of gravitational influence at 695,000 km distance, as we approach the singularity itself the gravitational force it exerts on us is going to increase exponentially as r decreases. Eventually, if the singularity is massive enough, we will get close enough that the gravitational force it exerts will become so great that the required escape velocity will be more than the speed of light in a vacuum. And since light can no longer escape the singularity’s pull, everything inside this radius will appear completely featureless and black to an outside observer. We now have our black hole.

It is important to note that the black hole is not the singularity. The singularity is merely the bit in the centre where all the mass is, while the black hole is everything encompassed inside this region of space that we cannot see. The border of the black hole is defined by the event horizon — so called because we can’t see any event that happens past it, just like we wouldn’t be able to see somebody waving to us over the Earth’s horizon – but the event horizon is not the “surface” of the black hole. It’s possible for an object to fall past the event horizon and still have a perfectly good time in the few moments remaining to it until it hits the singularity. The event horizon merely marks the point of no return; the radius inside which you will at some point become part of the singularity no matter what you do.

How is the radius of the event horizon defined?

In its simplest form, by something called the Schwarzchild radius, which applies for a perfectly spherical non-rotating singularity. We can derive this from the equations for gravitational potential energy and kinetic energy; the radius of the event horizon will be the point where the gravitational potential energy of the black hole exactly equals the kinetic energy of the light, or

 where m is the “mass” of the light (light has no mass, but that doesn’t matter because that term’s going to be removed from the equation in a minute anyway), v is the velocity of the light (commonly expressed in physics as c, which is equivalent to 300,000 km s^-1), M is the mass of the singularity, R is the distance at which the gravitational force is acting (in this case equivalent to the Schwarzchild radius R_{c since} that’s the point at which kinetic energy equals gravitational energy) and h is the distance of the light from the gravitational souce (again, equivalent to R_c). Substituting these values into the above equation and cancelling out redundant ones gives us

which rearranges to

 Since c and G are constants, the radius of the event horizon is therefore directly proportional to the mass of the singularity, and Wikipedia has saved me the trouble of crunching numbers by telling me that this proportionality is equivalent to a radius of 2.95 km per solar mass. In other words, if you really did go to the trouble of scrunching the Sun up into a singularity, its event horizon – and therefore the radius of the black hole it would create – would be just 2.95 km from the centre.

 What’s interesting about the Schwarzchild radius is that increasing the mass of the singularity will increase the Schwarzchild radius on a linear 1:1 basis (i.e. one solar mass gives an Rc of 2.95 km, two solar masses gives an Rc of 5.9 km etc.), but it won’t do the same for the gravitational force that mass exerts at the Schwarzchild radius, since that is determined by

 The best way to illustrate this is as follows: if we plug in the values M_o (representing one solar mass) for M and 2.95 km for R_c, we get

If we then double M_o (and hence double R_c) we get

 Despite doubling the mass of the singularity the force our hypothetical singularity exerts at the Schwarzchild radius has been halved, since by doing so we’ve doubled the Schwarzchild radius as well and gravitational force diminishes in proportion to the inverse square of the distance from the source.

 The upshot of all this is that you may or may not be ripped apart before getting to the event horizon depending on the size of the singularity. A small black hole like our solar mass one would kill you well before you ever hit the event horizon since the Schwarzchild radius is so small, while you could get quite some way inside the event horizon of the supermassive black hole at the centre of the Milky Way before succumbing to tidal forces. Which brings me to…

What happens to you if you fall into a black hole?

Why, you die, of course! However, you do it somewhat earlier than you might think. You won’t survive long enough to splatter onto the surface of the singularity like a bug on a windshield, and you might not even make it past the event horizon; instead, sooner or later, you succumb to something called spaghettification.

Spaghettification is a rather comically unpleasant process where the immense tidal forces of the black hole stretch approaching objects out into very long, thin strands of matter kind of like spaghetti. Going back to the gravitational force equation mentioned above, the difference in the force exerted on either end of an object approaching the black hole will be

where G is the gravitational constant, M is the mass of the black hole, R is the distance separating the black hole and the bottom of the object, and L is the length of the object. Basically you’re subtracting the force the black hole exerts on the top of the object from the force the black hole exerts on the bottom of the object to find the tidal – or “stretching” – force. These kinds of tidal forces have a negligible effect on our day to day lives because the Earth doesn’t have much mass and we’re far enough away from its centre that we never even notice them; for a typical 170cm tall person walking around on the surface, the Earth will exert a tidal force of 5 x 10^-6 N/kg (in other words, your feet will be pulled towards the centre of the Earth 5 x 10^-6 m s^-2 faster than your head), which is tiny, and anyway the surface of the Earth stops things from going any further.

However, if you up the mass of the thing you’re walking around on things start to get a bit more noticeable. If we replace the Earth with a singularity with the mass of the Sun, and recalculate the tidal force for the same distance away from the centre of mass (6400km), we find that our hypothetical singularity will pull the average person’s feet away from their head with a tidal force of 1.7 N/kg – this may not sound like much, but it’s roughly equivalent to half the maximum acceleration of a Saturn V rocket. I’m not sure if this would be fatal because the breaking force of a person isn’t listed anywhere on the internet for some reason, but it would definitely be uncomfortable and it’d only get worse as you fell further towards the singularity.

Anyway, even a very very small Sun-sized singularity will exert extreme tidal forces on objects close to it. These tidal forces are so strong (they increase to infinity as an object approaches the singularity, so there’s no way of resisting it) that any object which falls into a black hole will eventually end up being stretched out into the spaghetti-like strands described above.

What about relativistic effects?

I’m not going to talk about relativistic effects inside the event horizon, because nobody really knows how those work and the best hypotheses we have are a little bit wack. As ever with relativity, though, you have to consider two frames of reference; that of an outside observer, and that of the unlucky person actually going through the even horizon. For the latter, everything seems normal, although since they will be looking at the black hole from the inside it will be impossible for them to determine when they’ve crossed the event horizon (black holes don’t look black from the inside since there’s a whole bunch of light trapped in there with you). For the former, the person travelling towards the event horizon will appear to get slower and slower as the gravitational potential of the singularity increases and time dilates (they will also be redshifted) and they’ll never actually appear to hit the event horizon. This phenomena has been used to varying levels of effect in a number of bad sci-fi shows, almost all of which got it completely wrong.

If no light can escape the event horizon, how do we detect them?

A number of different methods, mostly revolving around their interactions with surrounding matter. Sometimes we can detect them through their simple gravitational effect on nearby bodies, but more often we see some sort of exotic stellar phenomena that can only be explained by the presence of a black hole. X-ray binaries, for example, are thought to consist of one normal star that is being gobbled up by a companion black hole; as the black hole chews up the star the infalling mass releases gravitational potential energy and spits it out in the form of very strong X-ray emissions, making this particular types of black hole very luminous in the X-ray spectrum.

The accretion discs surrounding “active” black holes that are in the process of consuming matter create X-rays by way of a similar mechanism: friction within the disc causes angular momentum to be transferred outward, which causes the gas in the disc which has lost that momentum to fall inward, which releases gravitational potential energy, which heats the gas up, which eventually gets so hot it starts emitting electromagnetic radiation in the X-ray part of the spectrum. Accretion discs are also sometimes accompanied by relativistic jets of matter that are blasted out from the poles of the black hole (thought to be caused by the shape of the hole’s magnetic field); these jets can sometimes be hundreds of light years in length, so they’re relatively easy to stop.

I should stress that nobody has ever directly observed a black hole. If it’s not actively consuming matter it’s practically impossible to spot one; you could theoretically do it by looking for gravitational lensing effects – caused by the black hole bending light as it passes by the outer edge of the event horizon – but this has never been done in practice.  So for all we know the above phenomena could be alien firework displays or magic space rocks or something. The evidence pointing towards the concrete existence of black holes is largely theoretical, albeit very convincing.

How are black holes formed?

Or the more popular version of this question I used to be asked a lot, which is “Will the Sun ever become a black hole?” It was encouraging since it was usually 12-13 year old kids doing the asking and it showed they had grasped some of the basics of how black holes form, but the actual mechanism is a little bit complicated. Basically you need some way of squishing a lot of mass up really really small, and the commonly accepted way of doing this is via a supernova. And since supernovae are an entire post all by themselves, this thrilling cliffhanger seems like as good a place as any to stop. BUY THE SEQUEL! COMING SOON (on Thursday).

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