Black Holes

Before you start to read this section - it's going to get complicated!  If you can handle that, then read on.

From reading the previous notes you will remember that a white dwarf star cannot be greater in mass than 1.4 times that of the sun, because above that mass, gravity would overcome what is called the "Degeneracy Pressure" and the star would collapse into a compact ball of neutrons.  The value of 1.4 x solar mass is known as the Chandrasekhar Limit, after the astronomer who first established that the limit exists.  Well, it is also been learned that the mass of a Neutron Star has a similar mass limit, above which a further collapse occurs and the object becomes a Black Hole.  The precise limit has not yet been established, but it is known to be less than three solar masses.

So what causes a black hole to form?

A black hole originates from the collapse of the iron core which forms in the late stages of evolution of a massive star, before the star finally goes supernova.  You will remember that any star with a very large starting mass - perhaps more than about ten times our sun, will ultimately undergo a supernova explosion, blowing most of the residual mass out into space.  The collapsed core which is left behind following the explosion is normally a neutron star, and we related elsewhere how these stars are very compact and spin at high speed.  However, theoretical models show that the most massive stars may not succeed in blowing all of their outer layers away in the explosion.  If enough matter falls back onto the core, raising it's mass above the neutron star limit, then the essence of what holds a neutron star together - a property called the Neutron Degeneracy Pressure - will be insufficient to counteract the effects of gravity.  A core whose mass exceeds the neutron star limit will continue to collapse catastrophically, and this time, instead of the heat and pressure generated by the collapse working to overcome the effects of gravity, they actually strengthen the gravity in the core.  This is because of the famous Einstein equation which you will all remember from your school days says that E=mc2. 

What this equation really means is that energy is equivalent to mass, and although in most normal cases the gravity of pure energy is negligible, in a collapsing neutron star this is no longer the case.  Here, the energy associated with the temperature and pressure concentrated in the tiny core acts like additional mass, hastening the collapse.  To the best of our current understanding nothing can halt the crush of gravity, and a black hole is formed.  So, what exactly is a black hole?

The idea of a black hole was first suggested as long ago as the late 1700's by the British philosopher John Mitchell and French physicist Pierre Laplace.  It was already known from Newton's Laws that the escape velocity from any object depends only on it's mass and size.  For a given mass, the more compact an object, the higher its escape velocity.  Mitchell and Laplace speculated that in the case of objects so compact that their escape velocity would exceed the velocity of light, no light would be able to leave them.  And then along came Einstein, who discovered that black holes are extremely bizarre objects, because space and time cannot be regarded as separate, but rather they have to be considered together in a thing called "Space-time".  Einstein showed that what we perceive as gravity arises from the curvature of space-time, a concept which is very hard to grasp because we cannot even visualize four dimensions, let alone visualize their curvature.  But we can draw an analogy to the curvature of space-time using a diagram to show how a rubber sheet might be affected by a massive object.

What this diagram is supposed to show is that the flat plane of space-time is distorted when a massive object is encountered.  The amount by which space-time is curved (the extent to which the object "penetrates" the rubber sheet) depends on it's mass.  For a very massive object, space-time is stretched so much that it becomes a bottomless pit, and a black hole is effectively a hole in the observable universe.  The boundary between the inside of the black hole and the universe outside is called the Event Horizon.  Within this event horizon the escape velocity exceeds the velocity of light, so nothing - not even light - can get out.  A black hole has an event horizon because, according to general relativity, light always follows the straightest possible path through space-time.  If space happens to be curved, as it is near to a black hole, then the path of a light beam will also be curved.

The radius of the event horizon for the black hole is known as the Schwarzschild Radius, and it depends on the mass of the black hole.  The greater the mass, the larger the radius.  One of the most common misconceptions about black holes is that they "suck".  For the record, black holes do not suck.  Newton's laws of gravity tell us that the allowed orbits in a gravitational field are ellipses, hyperbolas and parabolas - note that sucking is not included!  A spaceship or any other object would only get into trouble if it came very close to the black hole - within about three times it's Schwarzschild radius.  Only then would the laws of gravity deviate significantly from Newton's law, and a spaceship or other object approaching the black hole further out than this would simply swing around it in an ordinary orbit.  In fact, because most black holes are going to be very small, with typical Schwarzschild radii smaller than a planet, a black hole has got to be one of the hardest things in the universe to fall into by accident!

However, some of the strangest things happen as you approach a black hole.  One of them is that any light which does escape from the area is red-shifted, which means that the light is stretched to longer (redder) wavelengths by the gravitational forces.  This effect should not be confused with the Doppler effect, when light is stretched to longer wavelengths or squeezed to shorter ones by movement of an object.  This stretching by gravity is very different.  The other significant thing which happens as you approach the black hole is that time slows down.  If you were one of two astronauts on a mission and both of you were carrying clocks, if one of you approached the black hole your clock would lose time with reference to the one being carried by your colleague.  If you were able to communicate you would be able to see that this effect becomes more and more pronounced the closer you get to the black hole.  For you, everything would appear to be happening normally where you were, but as you looked backwards at your colleague his time would seem to be increasingly speeding up relative to you.  These strange effects would continue until you reached the event horizon, at which point your colleague would note that for you time had stopped!  This is really weird, and even more weird is that, according to theory your colleague would never actually see you disappear into the black hole.  It would take an infinitely long time to do so.  But for you things would be over quite quickly.  You would pass through the event horizon and disappear from this universe forever.  You wouldn't survive of course, because the gravitational gradient is so steep near to a black hole that over the distance from your head to your toes there would be enough of a difference of gravity that your body  would be stretched beyond its ability to cope.  You would be "Spaghettified!"

Latest News - January 2006
A spinning black hole in the constellation of Scorpius has created a stable dent in the fabric of space-time, scientists have observed recently.  The dent is the sort of possibility predicted by Albert Einstein’s theory of general relativity and it affects the movement of matter falling into the black hole.  The space-time 'dent' is invisible, but scientists deduced its existence after detecting two X-ray frequencies from the black hole that were identical to emissions noted nine years ago.  It's all linked to something called 'blinking X-rays'. 

As was explained above, black holes form when very massive stars runs out of fuel.  Their cores implode into a point of infinite density and their outer layers are blown away in a powerful supernova explosion.  Within a theoretical boundary called the event horizon, the black hole’s gravity is so strong that nothing, including light, can escape.  The X-ray frequencies detected by the team of researchers came from outside the event horizon of GRO J1655-40, a black hole located roughly 10,000 light-years from Earth. It is about seven times more massive than the Sun and syphoning gas from a nearby companion star.  But GRO J1655-40 undergoes short periods of intense X-ray emissions, followed by longer periods of comparative quiet. and scientists think this blinking pattern of X-ray activity is related to how matter accumulates around the black hole.

The theory is that gas syphoned from the companion star builds up steadily in an accretion disk around the black hole, the process continuing for several years.  While the accumulation is taking place, the black hole consumes very little gas from the disk.  Every few years however, something—scientists aren’t sure what—triggers a sudden binge fest on the part of the black hole, causing it to guzzle down most of matter in the disk within a period of only a few months.  Black holes emit millions of times more X-rays during these periods of increased activity than when they’re quiet.

In recent years, NASA’s Rossi X-ray Timing Explorer has caught GRO J1655-40 binging twice, once in 1996 and again in 2005.  Among the X-ray frequencies observed in 1996 was one at 450 Hz and one at 300 Hz.  These two frequencies were observed again in 2005.  This was surprising because when it comes to X-ray emissions, black holes are not known for stability.  X-rays are emitted from particles of superheated gas as they swirl into a black hole and rub against each other.  However, the luminosity and the frequency at which the X-rays flicker varies from moment to moment because the rate at which the black hole consumes the gas is not constant.  Therefore, detecting two stable frequencies nine years apart strongly suggests they are not caused by fluctuations in the black hole’s gas consumption, but by something else.  Scientists say that because it’s very hard to get gas to behave the same way twice, it argues strongly that these frequencies are being anchored by the black hole’s mass and spin, fundamental properties of the black hole itself.   Because the black hole is so massive and spinning so fast, it warps space-time around it.  This latest finding will allow scientists to calculate the black hole’s spin, a crucial measurement necessary for describing the object’s behavior.

Evidence for Black Holes
It's rather difficult to detect black holes, because of course we can't see them.  They emit no light and so we must look for the effects which they might have on any surrounding objects.  Black holes in close binary star systems should perhaps be the easiest to see, because of the effects which they have on their orbiting companions.  One of the most promising candidates for a black hole is a system called X-1 in the constellation of Cygnus.  This system contains an extremely bright star with an estimated mass 18 times that of our sun, orbiting an invisible object which has a mass about 10 times that of our sun.  The presence of the unseen companion can be proved by an analysis of the Doppler shift of it's spectral lines.  Add to this information the fact that detailed studies have shown the invisible object to be very small in size, and we are left with the inescapable conclusion that it has to be a black hole.

Another way of detecting the probable presence of black holes is that as material falls into them it is thrown into a rapid spiral orbit around the event horizon.  This causes the accelerated material to become highly excited, and the active region emits all kinds of radiation.  The centers of some galaxies are thought to harbor objects known as supermassive black holes and their presence has been deduced only by the presence of a disk of material in very rapid motion near to the center of the galaxy.

Do We Need To Worry
Actually, no.  Compared to the many other things which threaten our existence, being adversely affected by a black hole which happened to be roaming past is way down on the list of dangers.  We are actually at far more risk from a large meteorite impact, or a nearby supernova - or perhaps the risk of us extinguishing ourselves by our own actions is the greatest risk of all - but I've said this elsewhere and don't want to sound boring.

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