Stellar Evolution 

Stars form from the contraction of a gas cloud. This cloud will heat up as it contracts and thereby start emitting a faint red light. This will be a Protostar  .

If the cloud keeps on contracting, and if the cloud is massive enough, the core will eventually reach 10 million degrees, nuclear reactions will start, and a star comes into being.

A Hydrogen-burning star will occupy a place on the Main Sequence, its exact position being determined by its mass. 90% of all stars belong to this froup.

Note that as you ascend the Main sequence, the mass of the stars increase. This increased mass will mean a) more hydrogen is being burnt producing a brighter star, which then b) means that higher mass stars will have a shorter lifetime on the Main Sequence than less massive stars. This effect is accelerated by the more efficent nuclear reactions that the more massive stars are able to generate (the CNO cycle - the Carbon-Nitrogen-Oxygen cycle).

This characteristic can be used to calculate the age of a cluster. A Hertsprung-Russell diagram for the stars in a cluster will show a definite upper limit for Main Sequence stars, all stars more massive than this having ended their Hydrogen burning existence already.

This upper limit of main-sequence lifetime is referred to as the turn-off (see the diagram below, for the Pleiades and the Hyades).

You can see that the Pleiades are quite young with most stars still on the Main Sequence - the Seven Sisters themselves are not, however.

Following on from what we have just said, smaller stars are much more numerous than other types of stars (but this does not mean that fewer massive stars are being formed in the first place - just that the brighter stars have shorter lifetimes).

The HR diagram seems to show that the maximum mass for a Main Sequence is about 60 times the Solar Mass. The minimum mass of a star is about 0.1 of a Solar Mass, i.e. the mass required to produce nuclear reactions in the core. The surface temperture varies from 2000 to 35,000K degrees.

When the hydrogen fuel in the core is depleted, the core starts contracting and all other things being equal, you would expect that it will contract until conditions become of such intensity that the helium can start undergoing nuclear reactions.

However before this happens, hydrogen in the shell around the core is 'ignited' under the new conditions in which it finds itself (in fact the shell becomes so hot that fusion proceeds via CNO reactions). The effect of this 'shell-burning' is to cause the star to expand - it starts to become a Red Giant. As it expands, the energy given off by the star per unit area necessarily drops, lowering the surface temperature and consequently changing its color to red. Despite having a low temperature, they are still very bright by virtue of their size - their total energy output is still enormous. Looking at it another way, the actual output is governed primarily by nuclear reactions in the center, not by how large the envelope is.

Helium burning will eventually switch on - via a fusion process known as the 'Triple-Alpha' process because three helium nuclei fuse to form carbon.

One extra feature can be mentioned here. In its way to becoming a Red Giant, the helium core takes on a state of matter known as degeneracy. This is a quantum-mechanical state and suffice it to say here that when helium fusion starts, the degenerate core is unable to expand like 'normal' matter. This expansion in a normal star acts like a 'safety valve', reducing the temperature and lowering the rate of fusion. A degenerate core, on the other hand, suffers a runaway effect unable to reduce its temperature, leading to a so-called helium flash. This helium flash last only a few seconds but it destroys the degeneracy and the core is thereby eventually able to resume 'normally' again and thus adopt a stable configuration. Because the helium core has now expanded with the onset of helium fusion, hydrogen shell reactions are reduced but do not disappear altogether. This reduction of hydrogen burning causes a contraction of the star and a drop of luminosity by a factor of about 100 in comparison with its luminosity at the time just prior to helium flash.

Lower mass stars will be unable to fuse the carbon in their cores. They will proceed from top right of the H-R Diagram to the bottom left, becoming a White Dwarf.

Along the way, instabilities will cause them to eject their outer layer as a Planetary Nebula. These nebulae are probably less than 50,000 years old because after 100,000 years, the envelope becomes too thin to be seen. The name 'Planetary Nebula' stems from William Herschel for the reason that he perceived them to be disk-like, similar to a proper planet.

White Dwarfs are 'held up' by electron degeneracy, the quantum mechanical phenomenon discussed under 'Red Giants' for the case of helium degeneracy. There are no thermal reactions to stop the star from collapsing.

An unusual feature of this degeneracy is that the more mass the White Dwarf possesses the smaller it is. There is in fact a limit to how massive a White Dwarf can be, the Chandrasekhar Limit. For masses above this Chandaresekhar Limit, the electron degeneracy is unable to stop the star from collapsing. The limit is often stated to be approximately 1.4 Solar Masses - in practise, rotation will raise the limit to maybe 2 Solar Masses.

There are no White Dwarfs close enough to be seen with the unaided eye. The closest is Sirius B. This was 'detected' early in the nineteenth Century because of its gravitational effect on Sirius. It was first seen in 1862, although it was not appreciated for what it was until the 1920s.

Stars more massive than the critical value will fuse carbon in their core and proceed with further nuclear reactions until they have a core of iron. It is impossible to derive energy from the fusion of iron, the fusion of iron actually requires energy to be absorbed.

The idea of a Neutron Star originated theoretically 50 years ago. Pulsars, which were first discovered in 1967, are now identified as being Neutron Stars.

Jocelyn Bell discovered Pulsars in 1967 while a Graduate Student at Cambridge University.

The pulsar in the Crab Nebula rotates 30 times a second. It is a pulsar in light as well as in radio waves.

When it was discovered the Crab Pulsar was the fastest which was not surprising because it was also the youngest - pulsars slow down as time passes. Then pulsars reaching frequencies of the order of 600 times a second were discovered, although these are now known to be neutron stars in binary sysytems.

PSR1913+16 - the 'Binary Pulsar' was a discovered by Russell Hulse and Joseph taylor in 1974. It has a period twice that of the Crab (60ms), othe beam from only one of the pulsars being directed towards Earth. The two stars are separated by less than the solar diameter and orbit each other in 8 hours. This object is still known as the Binary Pulsar although nowadays more than twenty similar binaries are known.

All those pulsars whose masses can be measured accurately via radio pulsations are of approximately 1.4 solar masses

could be detected by X-Rays