This work was created by Dr Jamie Love and Creative Commons Licence licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Black Holes

by Dr Jamie Love Creative Commons Licence 1997 - 2011

What happens if you have a super, supergiant? You know - very massive.

Normally the neutron degenerate pressure stops the star's collapse and the material rebounds off the core as a Type II supernova leaving behind a neutron star. However, if the star is very massive it may not produce an outburst when its fuel burns out and it may not leave behind a neutron star. Instead it will continue to contract, squeezing its mass smaller and smaller and becoming denser and denser as it shrinks.

As the star shrinks it passes a point of no return. You see, the closer you get to the center of a mass, the more powerful its gravitational attraction becomes. At some stage during contraction the gravitational attraction on the surface of the collapsing star may become so great that nothing can escape from it. When a massive star reaches this small size the star's escape velocity, the speed needed to leave the surface, exceeds 300,000 kilometers per second. That's the speed of light and NOTHING can travel faster than the speed of light. (It's not just a good idea. It's a universal law! )

This "point of no return" is called the Schwartzchild radius and it depends upon the star's final mass. The more massive an object the larger its Schwartzchild radius.

For example, you would have to squeeze the mass of the Earth into a sphere with a radius of one centimeter in order to make it so dense that light could not escape from its surface. So the Earth has a Schwartzchild radius of one centimeter. But the Earth will never become a black hole. We can calculate the Earth's Schwartzchild radius to be one centimeter but the Earth will never reach it because it cannot put on "the big squeeze". It doesn't have enough mass.

Calculations have been made to figure out the minimum mass needed to contract an object below its Schwartzchild radius. (In a sense, these calculations are like Chandrasekar's work, but focus on matter's gravity instead of matter's degeneracy.) An object must be at least three times as massive as the Sun (three solar masses) to squeeze itself so small that it contracts below its Schwartzchild radius. Such a mass would have a Schwartzchild radius of 9 kilometers. In other words, if a supergiant retained three solar masses as it contracted, and it passed through the core neutron degeneracy limit without going supernova (thus retaining all 3 solar masses), it would contract to about 9 kilometers in radius.

If you are particularly interested in the math, the Schwartzchild radius (in kilometers) is given by the equation
Rs = 2GM/c2
G is the gravitational constant (something all professional physicists understand - or at least they pretend to understand it) and it equals 6.664 x 10-11 Nm2kg-2,
c is the speed of light (almost 3 x 10 8 meters per second)
and M is the mass (measured in kilograms) of the object whose Schwartzchild radius you want to know.
The gravitational constant (G) and the speed of light (c) are both constant and it is easier to measure stars in solar masses rather than kilograms. When you substitute those constants and express the mass as a solar mass, that equation becomes
Rs = 3(M) in kilometers. [Remember that this M equals the mass of the object divided by the mass of the Sun.)
From that simple equation you can determine the Schwartzchild radius of anything - the Sun, the Earth, the Moon and even yourself! Of course, none of those objects have enough mass to do all that squeezing (but it's fun to know). Remember, you need a non-fusing object (that's an object not undergoing nuclear fusion) of more than three solar masses to produce enough gravitational force to squeeze all that mass to its Schwartzchild radius.

The Schwartzchild radius is also called the event horizon because any event within the Schwartzchild radius is an event we can never see. It's "over the horizon". That's because anything within the Schwartzchild radius, including light, is dragged down to the mass at the center. Any object that becomes smaller than its Schwartzchild radius (passes its event horizon) will become a black hole.

To put it another way, a black hole forms when a star retains sufficient mass (at least 3 solar masses) to collapse to its Schwartzchild radius, dragging itself over its event horizon. The star still has mass so any object, like another star or a spaceship, could orbit a black hole just like it could orbit anything else. But it would be a very interesting ride!

If a star, spaceship or anything else got too close, as close as the black hole's Schwartzchild radius, the object would instantly be sucked over the event horizon and into the black hole, never to be seen again! [But even that is open to speculation because things don't happen instantly near the event horizon. As you will see shortly, it's all "relative"!]

Cool! What's in a black hole?

Mass! And lots of it.

We cannot see what goes on in a black hole because nothing, not even light, can get out. All we can do is speculate (guess) about what goes on within the event horizon.
Most scientists agree that the "stuff" inside the event horizon will continue to contact until what is left of the star has been squeezed into a single point. A point has no volume or size so this mass at the center of a black hole is called a singularity. We can never be sure what lies beyond the event horizon but a singularity is likely to be there.

Remember that I mentioned (in the neutron star lesson) that there might be an object more dense than a neutron star? Well, it depends upon your definitions and your desire to have an argument. Obviously a black hole has a lot of mass crushed inside a very small volume. Remember the smallest black hole formed from a dead star has three solar masses inside a 9 kilometer Schwartzchild radius. A neutron star, you'll recall is less than three solar masses inside a radius of 10 kilometers. Therefore you would be right to argue that a black hole is denser than a neutron star. Right? Well, not really. The problem is with that "singularity" and the math that it produces. You see, density is defined as the mass divided by the volume. If an object has zero volume, as does a singularity, than to calculate its density you must divide by zero. That's an "illegal operation" (on my calculator) and your math teacher will give you a hard slap on the knuckles if you try to divide by zero! Some might argue that a black hole has "infinite" density but that just doesn't cut it. For example, if the hole was infinitely dense its gravity would be infinite and we would have been dragged into the first black hole instantly (long ago). There are other problems with this type of thinking but I won't go into it (because I am not educated enough to give it a proper defense).

On the other hand, it is not beyond me to criticize some folks. Some scientists, especially those with a great deal of imagination, have speculated that the material which slips into a black hole reappears through a "white hole" somewhere else in the universe, perhaps even traveling through time as well as through space in order to get there! What an exciting idea. Too bad there is no evidence for it.

You could argue that "Puff the Magic Dragon" lives in a black hole and be confident knowing that no one will ever prove you wrong because we will never know! Is there a white hole on the other side of a black hole? Maybe. Maybe not. Like Alice following the White Rabbit into his hole, theoretical physicists find that once their ideas slip over the event horizon nothing makes sense. Some folks have interpreted that to mean that anything goes!

Slightly more "down to Earth", but only slightly, is the idea that the universe is full of mini black holes left over from the Big Bang (the creation of the universe). These objects, if they exist, are calculated to have a mass of 1011 kilograms and a radius of about 10-10 of a meter (an angstrom). That's about the size of an atom. One day such a mini black hole might be detected, using a method described below, but until then they are only a dream.

The physics of black holes is complicated, highly mathematical and deeply embedded in two of the most powerful, amazing and difficult areas of physics - relativity and quantum mechanics.
One idea from the quantum mechanical field is that black holes will lose energy by ejecting particles along their Schwartzchild radius. Eventually these holes would disappear - they would just evaporate!

Hey, I thought nothing could get out of a black hole!

Right. Sort of. This escape of particles from a black hole has to do with a weird part of quantum mechanics.
["You mean there's only one weird part to quantum mechanics?!"]
Out of nowhere, out of nothing, pairs of particles are created and then immediately destroyed. This sounds crazy but there is actually some experimental evidence to support this idea!
[For those wanting to get really excited about "weird science", do a search with the keywords "zero potential energy, vacuum energy, and Z energy". But don't come back to me to explain it! ]
Anyway, this magical creation and instant destruction of these particles may be occurring at the event horizon. Maybe the pair is created right at the edge of the event horizon such that one particle stays inside and the other escapes. Given enough time, enough particles escape this way and the back hole disappears.
At least, that's the way the story goes.

A great deal of amazing physics should occur in the neighborhood of the event horizon, just outside the black hole, and this physics is well accepted and likely to be correct. The gravity around the event horizon is so great that local space and time should be distorted, contracted, as you approach the horizon. Due to the effects of relativity, you would not notice anything peculiar happening to you as you approached the event horizon but an observer (safely far away) would see you becoming stretched out like a piece of gum. Also, that observer would see that you are slowing down. This time dilation would become more obvious (to the observer) as you approached the hole and from the observer's position it would appear that your time has come to a full stop once you had met the event horizon.
From your perspective, however, it would appear that the observer, and everything else in the rest of the universe, had speeded up.

All that is pretty neat but there is one problem when falling towards the event horizon. The gravitational force very quickly becomes unbearable. The difference in force between one part of your body and the other would cause you to be torn apart! Exactly how that would happen is best left to your imagination. On the other hand, you would have been long dead anyway from the incredible amounts of radiation most black holes produce (as explained shortly).

Sounds awful. What a shame too! I thought there might be a way to use a black hole for space travel.

Well, maybe there is.
I have been explaining the physics of a Schwartzchild black hole - a black hole that is not rotating. There have been speculations about rotating black holes, called Kerr black holes, that might twist the laws of physics just enough to make science fiction writers happy. Unfortunately, there is little I can teach you about them because their physics is far beyond me!

Do black holes really exist? How would you find one?

The math and physics indicate that black holes are very likely to exist, but PROOF is not easy to come by. (Proof is in the eyes of the beholder.) There is every reason to believe that black holes really do exist because there is a lot of supporting evidence. Indeed, black holes seem to be the only thing that can come of a non-fusing object that is more than 3 solar masses.

You really can't see a black hole but you should be able to sense a black hole by the one thing it certainly does have - MASS! Three ways of detecting black holes are worth mentioning.

  1. A star orbiting a black hole (outside its event horizon, of course) will circle it at a very fast rate. This has to do with a well-understood branch of physics called "orbital mechanics". The math isn't too difficult to learn (simple algebra) but I'll skip it all here. Naturally the black hole will be invisible but its rapidly orbiting star companion will give away its location. In 1994 a team of astronomers announced that they had found a star rapidly circling an invisible companion. When they applied the math rules of orbital mechanics to the star's period of orbit, they determined that the mass of the hidden object was between 5 and 10 solar masses, well above the 3 solar masses needed to make a black hole. That's not proof of a black hole but pretty good evidence.

  2. Light from a distant star passing near a black hole will be bent from its normal path. This is due to the relativistic effects that gravity has on light. This effect was predicted by Einstein and proven by Eddington. (Remember Eddington? Gee, he got around! ) This bending causes a distortion in the light and a double image of the distant star will be produced. Again, the math is not that difficult (simple geometry). Several astronomers have reported observing such events, but it is unclear if a black hole has caused the distortion or simply a mass below Chandrasekar's limit has caused it.

  3. Any matter around a black hole will be drawn into it by the hole's powerful gravity. Rather than falling directly through the event horizon, most material will spiral into it. That means a black hole's event horizon can have an "edge" made of materials being sucked into the hole. (Some sci-fi movies show this effect and it looks like water going down a drain.) As materials spiral towards the event horizon they bump into other materials. This causes friction, friction causes heat and this heat can escape if it hasn't yet reached the event horizon. This heat is actually photons of light and the energy of that light can become very high energy. Indeed, just before the material reaches the hole's Schwartzchild radius, it will have picked up so much frictional heat that it will emit the energy as X-rays! In order to find a black hole, simply look for powerful sources of X-rays. (And rule out any other likely sources for the X-rays such as pulsars.)
OK. Where might I find a likely black hole candidate?

The best candidate I know of is a powerful X-ray source called Cygnus X-1. Not only is it considered by astronomers as our best bet for a black hole, but it also gives me an excuse to teach you some more constellations!

Last month we finished your lesson with Vega in the constellation of LYRA because that was an exceptionally bright star in the eastern sky. Now that the sky has rotated a bit further we are finding the summer constellations coming into view.

To the east of LYRA is CYGNUS the Swan. The Swan's outstretched wings produce an obvious X-shape to this constellation and you are unlikely to mistake it with anything else.

Its brightest star, Deneb, has a magnitude of 1.25 so it stands out. This star is actually a white supergiant with an absolute magnitude over 70,000 times as luminous as our Sun. It's over 1800 light-years away but it's so bright it looks like it is just next door. Sadar is at the center of the swan (the center of the "X") and is another supergiant over 6,000 times as luminous as the Sun.

If you continue along the line the next star you come to is Eta Cygni in the throat of the Swan. [The symbol for "eta" is . I think it looks like a fancy "n" but I've been told it is equivalent to an "h"!] If you go past it you come to a similar looking star called Chi Cygni. [It's symbol is and it looks like an "x" but it is NOT Cygnus X-1.] There are two reasons why I point out Chi Cygni to you. First, it's a strange star that varies in magnitude from as low as 14.2 to as high as 3.3. Next month I'll explain how that happens but, until then, understand that Chi Cygni may or may not be visible and that brings us to the second reason I point it out to you. If you see two stars in this part of the sky, the first one (down from Sadar) is Eta Cygni but if you see only one star, then it must be Eta Cygni (and Chi Cygni must have dropped below a visible magnitude).

OK, I can see Eta Cygni. Now what? (So what?)

Cygnus X-1, a likely black hole, lies in the neighborhood of Eta Cygni. Of course, you can't see it even with the best telescope but with a little magnification you might see its companion - HDE 226868. It's about 5000 light-years away but it is so bright that it has a magnitude of about 9. HDE 226868 is a B-type supergiant. It's massive (30 times the mass of the Sun) and big (about 9 million kilometers radius) but most importantly, it seems to be orbiting an invisible companion. Based upon the orbital period of HDE 226868 (5.6 days) astronomers have estimated that its invisible companion has a mass of about 14 times that of our Sun. So HDE 226868 is rapidly orbiting something that is very massive yet very dark. Hmm.

That alone is not enough to convince me that HDE 226868 orbits a black hole but the X-rays emitted are good evidence. That's how Cygnus X-1 got its name. It emits huge amounts of X-rays! Astronomers believe that Cygnus X-1 is pulling away the outer layers from HDE 226868. That material spirals inwards creating a rotating disk around Cygnus X-1. The material gets heated from the friction and energy of falling (gravitational energy) to the point that the material gives off X-rays. Of course, normally when you heat an object it gives off low energy as infrared so the energy around Cygnus X-1 must be very, very high. Indeed, calculations are consistent with the idea that the material emits its last energy to the universe as it falls over the event horizon. Yes, the X-rays from Cygnus X-1 are that material's "swan song"!

I think it's nice to know that only 5000 light-years away, near Eta Cygni, is a likely black hole. There may also be a black hole at the center of some galaxies including our own. We'll come back to galaxies in a future lesson and then I will show you how to find the center of our galaxy. Meanwhile, let's finish our observations for this month.

Below CYGNUS is another bird constellation, AQUILA the Eagle. It's brightest star, Altair, is only 16.6 light-years away and is ten times as luminous as our Sun. In our sky it has a magnitude of 0.8.

I mentioned a star's spin earlier. Well, careful measurements of Altair's rotation rate show that it spins so fast that the force must cause this star to have a distorted shape. It literally bulges at its equator! Unfortunately, even the most powerful telescopes can't yet see the bulge. Altair is flanked on either side by a pair of fairly bright stars and the rest of the constellation of AQUILA is made of much fainter stars.

All astronomy students learn that Vega, Deneb and Altair make up the pseudoconstellation called the "Great Summer Triangle". Like the Big Dipper, the Great Summer Triangle is not an official constellation but it stands out so well in the summer night skies that it is as familiar to star gazers as ORION is in the winter. Note that the Great Summer Triangle is made from three bright stars from three different constellations and it is an outstanding object in the northern sky.

I hope you now understand that very large stars, supergiants, are made of layers of different nuclear fusion reactions with degenerate iron accumulating in the core. When its fuel runs low a supergiant usually goes supernova (Type II). The material created by the explosion of a supernova can go on to form new nebulas and eventually make planets and all the things that might exist on a planet, including life.
If the core retains a mass between 1.44 solar masses (Chandrasekar's limit) and 3 solar masses, it will become a neutron star. Neutron stars are amazingly dense objects made mostly of neutrons. If a neutron star has a magnetic axis off-center from its spin axis it will emit pulses of light as it spins and will be called a pulsar.
Any (non-fusing) mass greater than 3 solar masses should become a black hole. The incredible mass of a black hole creates an event horizon through which nothing, not even light, can escape. The radius of a black hole's event horizon, its Schwartzchild radius, is determined by the mass of the core that remains. The smallest black hole produced by a dead star would have a mass three times that of our Sun and a Schwartzchild radius of 9 kilometers. Amazing physics occurs in the neighborhood of an event horizon, but that has to do with relativity and quantum mechanics. No one knows what kind of physics goes on inside the event horizon and it is unlikely we will ever know!

Make a point to get out and find the Great Summer Triangle. Find the stars of AQUILA, CYGNUS and LYRA and remind yourself that Cygnus X-1, a likely black hole, is near Eta Cygni.

That concludes our little tour of the sky and your lessons on the weird and wonderful things that happen to a very big star when it dies. This would be a good time to take a break and contemplate what you have just learned, but be sure to finish this month's lessons by (eventually) reading the lesson on orbits.




This work was created by Dr Jamie Love and Creative Commons Licence licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.