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Black holes

Black holes are peculiar objects with many strange properties, but most books and articles have emphasised their exotic aspects, and obscured their fundamentally simple nature. The description given below was first worked out by the French mathematician Pierre Laplace in 1796, so they are not even a modern invention! Before discussing black holes themselves we should think briefly about gravity.


What is Gravity?

Physicists recognize that the whole of the physical world can be described in terms of four basic forces. Two of these are concerned with the innermost structure of atoms, and a third, the electromagnetic force, dominates the interaction of atoms with each other. The fourth, and by far the weakest of these forces, is gravity. It is therefore only significant when enormous numbers of atoms are collected together into objects the size of the Earth, or bigger. Gravity is the dominant force in the lives and deaths of stars and galaxies.

Any atom, or collection of atoms, has a property called mass, which measures how much material there is in the object. On the surface of the Earth, the gravity of the Earth pulls downwards on all masses giving the sensation of weight. On the surface of the Moon this pull, or weight, is only one sixth of that on the Earth, and so weight depends on where you are, whereas mass is an intrinsic property of all objects.

In the 17th century Isaac Newton described gravity by saying that each mass attracts every other mass in the universe with a force which depends on how much material is present and how far away it is. In 1915 Albert Einstein dramatically changed our idea of what gravity is, but Newton's description is adequate for this article.

So, gravity is a universal attractive force which causes objects to `fall' in the broadest sense, and tries to pull objects like stars and galaxies together. It is bound to succeed unless it is opposed by some other force.


What is a Black Hole?

If a ball is thrown upwards from the surface of the Earth it reaches a certain height and then falls back. The harder it is thrown, the higher it goes. Laplace calculated the height it would reach for a given initial speed. He found that the height increased faster than the speed, so that the height became very large for a not very great speed. At a speed of 40,000 km/h (25000 mph, only 20 times faster than Concorde) the height becomes very great indeed - it tends to infinity, as a mathematician would say. This speed is called the `escape velocity' from the surface of the Earth, and is the speed which must be achieved if a space craft is to reach the Moon or any of the planets. Being a mathematician, Laplace solved the problem for all round bodies, not just the Earth.

He found a very simple formula which tells us that the escape velocity, V, is given by,

v = (2GM/R)0.5

where G is a constant which defines how strong gravity is, M is the mass, or amount of material, in the body and R is its radius. This formula says that small but massive objects (i.e. small R and large M ), have large escape velocities. For example if the Earth could be squeezed and made four times smaller, the escape velocity would need to be twice as large. This surprisingly simple derivation gives exactly the same answer as is obtained from the full theory of relativity.

Light travels at just over 1000 million km/h (670 million mph), and in 1905 Albert Einstein proved that nothing can travel faster than light. The above formula can be turned around to tell us what radius an object must have if the escape velocity from its surface is to be the speed of light. The answer is,

R=(2G/c2)M

where c is the speed of light. This particular radius, R, is called the 'Schwarzschild radius' in honour of the German astronomer who first derived it from Einstein's theory of gravity. The formula tells us that the Schwarzschild radius for the Earth is less than a centimetre, compared with its actual radius of 6357 km. Values for some other astronomical objects are given in the table below.

It might seem surprising that light can be thought of as behaving like rocket ships and cricket balls! It was Einstein who showed that light can be considered as a collection of particles, called photons, which have mass, or more correctly energy, by virtue of the famous formula E=Mc2 relating energy (E) and mass (M). Photons always travel at the same speed, the speed of light, but when moving away from a gravitating object they lose energy and, to an external observer, appear to be redder. It is this 'red-shift' which means that photons from a black hole ultimately lose all their energy and become completely invisible.

If even light energy does not travel fast enough to escape (and nothing can travel faster), then no signals of any kind can escape and the object would be 'black'. The only indication of the presence of such an object is the pull of its gravity. Away from the surface this is just the same as if an ordinary object of the same mass were there. The presence of gravity means that objects can fall into it, and hence 'hole'.

So, a black hole is an object which is so compact that the escape velocity from its surface is greater than the speed of

Object

Mass
(Solar Masses)

Radius
(km)

Escape Velocity
(km/sec)

Schwarzschild Radius

Earth

0.00000304

6357 11.3 9.0mm
Sun 0.1 696,000 617 2.95km
White Dwarf 0.8 10,000 5,000 2.4km
Neutron Star 2 8 250,000 5.9km
Nucleus of Galaxy 50,000,000 ? ? 147,500,000 km

The speed of light is 299,800 km/sec (186,000 miles/sec). 11 km/sec is equivalent to 40,000 km/h (or 25,000 mph),

147,000,000 km is almost equal to the radius of the Earth's orbit round the Sun.


Where might we find Black Holes?

It is impossible to observe a black hole directly and so any black hole candidates have to be identified by their effect on the matter surrounding them. If no other explanation for the observed phenomena is valid then it is likely that a black hole is present.

There are some objects that are good candidates for the presence of a black hole.

  1. Any star shines and survives because the pull of gravity, which is trying to compress it, just balances the pressure generated by the nuclear furnace at its centre, which is trying to expand it. Once the furnace runs out of fuel, which must eventually happen, the pressure decreases, loses its battle with gravity, and the star collapses. Astronomers believe that one of only three things can happen to a star in this situation, depending on its mass. A star less massive than the Sun collapses until it forms a `white dwarf', with a radius of only a few thousand kilometers. If the star has between one and four times the mass of the Sun, it can produce a `neutron star', with a radius of just a few kilometers, and such a star might be recognised as a `pulsar'. The relatively few stars with greater than four times the mass of the Sun cannot avoid collapsing within their Schwarzschild radii and becoming black holes. So, black holes may be the corpses of massive stars.
  2. Most astronomers believe that galaxies like the Milky Way were formed from a large cloud of gas which collapsed and broke up into individual stars. We now see the stars packed together most tightly in the centre, or nucleus. It is possible that at the very centre there was too much matter to form an ordinary star, or that the stars which did form were so close to each other that they coalesced to form a black hole. It is therefore argued that really massive black holes, equivalent to a hundred million stars like the Sun, could exist at the centre of some galaxies.

How could we see a Black Hole?

Because black holes are small, and no signals escape from them, it might seem an impossible task to find them. However, the force of gravity remains, so if we detect gravity where there is no visible source of light then a black hole may be responsible. This type of argument, by itself, is not very convincing, and so we must look for other clues. If there is other material around a black hole which might fall into it, then it will. There is then a good chance that as it falls it will produce some detectable signal not from the black hole itself, but from just outside it.

Most stars are not single, like the Sun, but are found in pairs, small groups or large clusters. If a pair of stars have different masses then the more massive one will burn up its nuclear fuel and may become a black hole, whilst the other remains a normal star consuming its fuel more slowly. Gas can then be sucked from the remaining star into the black hole. The gas becomes very hot, with a temperature of millions of degrees, and will shine not with visible light but with X-rays. These X-rays will have an observable effect on the light output from the ordinary star. Since the star and black hole go round each other every few days, we might expect to see regular variations in the brightness and X-ray output.

There are some X-ray sources which have all the properties described above. Unfortunately it is impossible to distinguish between a black hole and a neutron star unless we can prove that the mass of the unseen component is too great for a neutron star. Strong evidence was found by RGO astronomers that one of these sources, called Cyg X-1 (which means the first X-ray source discovered in the constellation of Cygnus), does indeed contain a black hole.

Things are rather different if there is a massive black hole in the centre of a galaxy. It is possible there for a star to be swallowed by the black hole. The pull of gravity on such a star will be so strong as to break it up into its component atoms, and throw them out at high speed in all directions. Some of the fragments will fall into the hole, increasing its mass, whilst others could produce an outburst of radio waves, light and X-rays.

This is just the behaviour which is observed in galaxies of the type called 'Quasars' and may well be happening in a milder way in the centre of our own Milky Way.

Astronomers from the RGO were part of a team who found that the galaxy NGC 4151 contains about 1000 million times the mass of the Sun, concentrated in a nuclear region whose diameter is no more than 4000 times the distance between the Earth and the Sun. The most plausible explanation at present is that most of this mass is in a black hole at the centre.


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