White dwarfs, neutron stars, black holes: this is a list of objects in which each is smaller, denser and more extreme in its physical conditions than the one before. The compression is a result of the familiar force of gravity, but the condensed stars which result are outside our Earth-bound experience. A matchbox-sized piece of white dwarf material would weigh tens of tons, while the mass of a battleship in neutron star material occupies the space of a pinhead.
A white dwarf, which is a star about the size of the Earth but with a mass similar to that of the Sun, is prevented from shrinking further by 'electron degeneracy pressure' – under the laws of quantum mechanics, free electrons can be packed only so closely together and not more. In some stars, usually more massive than white dwarfs, this barrier is overcome when the electrons combine with protons to form neutrons, which can pack together 2000 times more closely. A neutron star has one and a half times the mass of the Sun, but is only about 20 kilometres across. Neutron stars are created when the core of a dying, massive star collapses, triggering the explosive ejection of the outer parts of the star in a supernova. Although neutron stars are so small and cannot generate light by fusion, some can be observed at great distances by an entirely different kind of radiation, a regularly pulsating radio signal. These are the pulsars.
What are pulsars?
Pulsars were discovered in 1967 by Jocelyn Bell and Anthony Hewish at the radio astronomy observatory (now the Nuffield Radio Astronomy Observatory) at Cambridge. Pulsar radio emission is very distinctive, a uniform series of pulses, spaced with great precision at periods of between a few milliseconds and several seconds. Over 700 radio pulsars are known. Some pulsars have also been detected by optical, X-ray and gamma-ray telescopes.
The regularity of the pulses is phenomenal: observers can now predict the arrival times of pulses a year ahead with an accuracy better than a millisecond. How can a star behave as such an accurate clock? The only possibility for so rapid and so precise a repetition is for the star to be very small, rotating rapidly and emitting a beam of radiation which sweeps round the sky like a lighthouse, pointing towards the observer once per rotation. The only kind of star which can rotate fast enough without bursting from its own centrifugal force is a neutron star.
Pulsars are rapidly rotating, very strongly magnetised neutron stars, with fields of strength reaching 1000 million Tesla (10 million million Gauss. For comparison, the Earth's magnetic field measures less than 1 Gauss). These extreme properties result from the compression of the original star's core, which would have had a weaker magnetic field and slower rotation. They make neutron stars into powerful electric generators, capable of creating and accelerating charged particles to energies of a thousand million million Volts. These particles are the source of the beams of radiation in radio, light, X-rays and gamma-rays. They also carry away much of the pulsar's energy in the form of a fast wind. Their energy comes from the rotation of the star, which must therefore be slowing down. This slowing down can be detected as a lengthening of the pulse period. Typically a pulsar rotation rate slows down by one part in 10 million each year: the Crab Pulsar, which is the youngest and most energetic known, slows by one part in two thousand each year.
How many pulsars in our galaxy?
Pulsars are found mainly in the disc of the Milky Way, within about 500 light-years of the plane of the Galaxy. A complete survey of the pulsars in the Galaxy is impossible as faint pulsars can only be detected if they are nearby. Radio surveys have now covered almost the whole sky, and over 1,000 pulsars have been located. Their distances can be measured from a delay in pulse arrival times observed at low radio frequencies; the delay depends on the electron density in interstellar gas and on the distance travelled. Extrapolating from the small sample of detectable pulsars, it is estimated that there are around 200,000 pulsars in the whole of our Galaxy, taking into account those whose lighthouse beams do not sweep across in our direction.
Each pulsar radiates for around 20 million years; after this time it has lost so much rotational energy that the particle creation process begins to fail and radio pulses are no longer produced. If we know the total population (200,000) and the lifetime (20,000,000 years), we can deduce that a new pulsar must be born in our galaxy roughly every 100 years (assuming that the population remains steady).
If pulsars are born in supernova explosions, then the rate of supernovae must be at least as high as the pulsar birth rate. In fact the supernova rate is probably also around one every 100 years or higher. Supernovae are spectacular events. The last directly observed supernova in our galaxy was Kepler's supernova of AD 1604, but we do know that others occur which are less spectacular or which are hidden from us by interstellar dust clouds.
The Crab Pulsar
The Crab Nebula is the visible remnant of a supernova explosion which was witnessed in AD 1054 by Chinese and Japanese astronomers. Near the centre of the Nebula is the Crab Pulsar, which is the most energetic pulsar known. It rotates 30 times per second, and it is very strongly magnetised. It therefore acts as a celestial power station, its wind supplying enough energy to keep all of the Nebula emitting radiation over practically the whole of the electromagnetic spectrum.
The Crab Pulsar radiates two pulses per revolution: this double pulse profile is similar at all radio frequencies from 30 MHz upwards, and in the optical, X-ray and gamma-ray parts of the spectrum, covering at least 49 octaves in wavelength.
The visible light is powerful enough for the pulsar to appear on photographs of the Nebula, where it is seen as a star of about magnitude 16. Normal photographs smooth out the pulses, but stroboscopic techniques can show the star separately in its 'off' and 'on' conditions. Images of the pulsar have also been made by the Hubble Space Telescope.
Binary pulsars and general relativity
Many stars are members of binary systems, in which two stars orbit around each other with periods of some days or years. A number of binary systems are known in which one of the stars is a neutron star. Some of the most spectacular are bright X-ray sources and are known as X-ray binaries or X-ray pulsars. In these systems, gas is being drawn from the outer layers of a companion star by the neutron star's gravitational pull. As the gas falls towards the neutron star, a large amount of energy is released, mostly as X-rays. X-ray binary pulsars, unlike radio pulsars, are powered by the infalling matter rather than the pulsar's rotation. They usually rotate much more slowly than radio pulsars and can be slowing down, speeding up, or do both at different times.
Not all pulsars in binary systems are accreting matter from their companion. These are detected as radio pulsars and most of them are `millisecond pulsars', which rotate much more quickly (hundreds of times per second) and have magnetic fields thousands of times smaller than normal pulsars. Millisecond pulsars have even more precise rotation periods than other pulsars and have extremely long lifetimes because they are slowing down only very slowly, around 1 part in 10 thousand million every year. There are probably at least as many of them in the galaxy as there are normal pulsars.
Many millisecond pulsars are in binary systems and it is believed that they are probably the end product of X-ray binary pulsars with relatively low mass companion stars. Very recently, X-ray observations have revealed millisecond rotation periods in X-ray binaries, making the final link with millisecond radio pulsars. The transfer of matter when the system is an X-ray binary speeds up the neutron star to millisecond rotation periods and leaves it eventually as a rotation-powered millisecond radio pulsar orbiting the remnants of its companion, often now a white dwarf.
The most famous binary radio pulsar is the Hulse-Taylor pulsar, PSR 1913+16, which has another neutron star as its companion. The pulsar is a normal radio pulsar, not a millisecond pulsar, with a rotation period of 59 milliseconds. The two stars are so close that their orbital period is less than eight hours, but no matter streams between them; they interact only by their mutual gravitational attraction. The orbit of the pulsar can be described in great detail because the arrival times of its pulses at the Earth are like the ticks of an accurate clock moving very rapidly in a strong gravitational field, which is the classical situation required for a test of Einstein's General Theory of Relativity.
According to non-relativistic, or Newtonian, dynamical theory, the orbits of both stars should be ellipses with a fixed orientation, and the orbital period should be constant. Measurements of the arrival time of the pulses have shown significant differences from the simple Newtonian orbits. The most obvious is that the orbit precesses by 4.2 degrees per year. There is also a small, but very important, effect on the orbital period, which is now known to be reducing by 67 nanoseconds (less than one ten-millionth of a second) each orbit.
The reducing orbital period represents a loss of energy, which can only be accounted for by gravitational radiation. Although gravitational radiation itself has never been observed directly, the observations of PSR 1913+16 have provided good proof of its existence. It is appropriate that this discovery, which is a further confirmation of the predictions of the General Theory of Relativity, was announced in 1979, which was the centenary of Einstein's birth.
Three Jodrell Bank scientists (Ingrid Stairs, Andrew Lyne and Setnam Shemar) have been studying 13 years' worth of data from the pulsar PSR B1828-11. This pulsar rotates 2.5 times per second, but, unlike any other, wobbles regularly with a period of about 1000 days. The motion is very much like the wobble of a top or gyroscope. This wobble, or precession, has two manifestations: it causes the observed pulse to change its shape, and causes the time between pulses to vary, becoming sometimes shorter, sometimes longer.
In an article in the 3 August 2000 issue of Nature, the Manchester astronomers argue that these variations imply that the neutron star, instead of being perfectly spherical, is slightly oblate. Stairs explains:
'The bulge in the neutron star causes the angle between the pulsar's rotation axis and its radio beam to change with time, creating the wobbling effect that we measure.'
Lyne emphasizes that the oblateness is incredibly small:
'This star departs from being a perfect sphere by only 0.1 mm in 20 km. On Earth this would mean that no mountain could be higher than 3 cm!'
The surprising aspect to the discovery is not the small size of the wobble, but that fact that it is seen at all. Astronomers know from other long-term observations, mostly done at Jodrell Bank, that a pulsar is made up largely of a neutron superfluid, with a solid crust. Current theories predict that the interaction between the superfluid and the crust should cause any precession to die out extremely quickly.
'But this pulsar is one hundred thousand years old, and it's still wobbling!' exclaims Lyne. 'We really don't understand how this precession can be happening, and theorists are going to have to do some work to explain it,' adds Stairs.