Stellar Evolution - Low Mass Stars:

If a star is too low in mass (less than 7.5% the mass of the Sun), it will not really be a star at all. Such objects never have a main sequence phase; they are brightest and hottest when they form (M spectral class), and then forever cool and get dimmer. They are called brown dwarfs. Below 6% the mass of the Sun, they do not even get hot enough to destroy lithium - this has provided one way of distinguishing them from low mass stars (which all destroy lithium) and hundreds are now known (though the first one was found only in 1995). Finally the brown dwarf will cool below the minimum main sequence temperature (about 2000K) and then its state is more obvious. The first such object was Gl229B, at about 1000K.

The evolution of stars up to about ten times the mass of the Sun are all similar to each other. After forming and reaching the main sequence, they remain there for a much longer time. During this phase they are burning hydrogen and increasing in brightness only a little. When the core is converted to helium, it can no longer produce energy and begins to collapse again. This raises its temperature and density, as well as that of the surrounding regions. Around the core, hydrogen can fuse again in a shell. This shell burning causes the outer parts of the star to swell, so the surface becomes bigger and cooler (the subgiant phase).
A more detailed story for a solar mass star is here.

More details on the next part can be found here.
The core becomes degenerate (electrons are forced into high energy states by a quantum mechanical principle); its pressure then is not thermal and does not respond easily to heat input. Shell burning continues to brighten the star and swell it (the red giant phase). When helium ignites, the increased heat does not expand the core but does make the helium burn faster. This runs away with itself in the "helium flash", until the core is so hot that the degeneracy is lifted. We do not see this flash as it is buried down inside the star. The star ends up responding by lowering its luminosity in non-degenerate helium burning and shrinking a little, leaving the tip of the red giant branch.
This "helium main sequence" can take the star over to the yellower "RR Lyrae" phase (where it pulsates) depending on its composition (a low fraction of heavy metals), or leave it near the red giant branch (for compositions like the Sun). As the helium core burns to carbon (triple-alpha chain) and begins shrinking again, the star brightens and swells  and the envelope of unburned hydrogen becomes increasingly less stably bound to the star. It finally cools enough to form dust, and the intense light from the core coupled with the dropping escape velocity (because the radius is getting so large)  causes the envelope to be ejected.
This phase produces what is call a "planetary nebula"; the expanding envelope leaving the star. The UV radiation from the hot core ionizes it and makes beautiful objects in the sky. Some products of the nuclear burning (C,N,O) and dust are injected into the interstellar medium, to await a new star formation phase. The core, unable to generate further energy, shrinks to the size of the Earth and becomes a "white dwarf" (see next lecture for more details).

Timescales for the Sun:
collapse from interstellar cloud - 10⁵ years
protoplanetary disk phase - 10⁷ years
main sequence phase - 10¹⁰ years
subgiant phase - 10⁸ years
red giant phase - 10⁹ years
planetary nebula phase - 10⁵ years
white dwarf phase - 10³⁵ years

Stellar Evolution - High Mass Stars:

This begins as above, except that the timescales are very much shortened. They differ at the helium burning phase, since the weight of the overlying star allows helium burning to occur before the core is degenerate. It also allows the burning to continue with carbon, and all the elements up to iron can be produced by nuclear fusion in the core. There will be formation of a succesive layer of shells, each going through the next heaviest cycle, as the core shrinks down. Because each heavier fusion cycle is less efficient, the time spent on each gets shorter. The final cycle leading to iron is only a few minutes long. No energy can be extracted from iron fusion (it costs energy), so the star is out of luck then. The core collapses, and the pressures are to great to even stop at the white dwarf phase. A supernova explosion immediately occurs, blowing off all the outer processed layers and leaving a neutron star or black hole in the center. (see next lecture for details)

Stellar Lifetimes:

It is fairly easy to estimate the main sequence lifetime of a star. It is easiest to do everything relative to the Sun. For the Sun, you can estimate its lifetime using the current measured solar luminosity, the amount of hydrogen which must be used up per second to produce that luminosity, and the amount of hydrogen available for fusion (the inner part of the Sun does not mix by convection and so does not drag down hydrogen from higher up). This gives a lifetime for the Sun of about 10 billion years (the actual number is closer to 12 billion years). Other stars' lifetimes will be proportional to that, modified by the ratio of their mass over their luminosity.
lifetime = 10¹⁰ years (M_star/L_star) [with M_star and L_star in solar units]
Thus, a star which has ten times the mass of the Sun, but ten thousand times its luminosity, will have a lifetime a thousand times shorter (or 10 million years). Massive stars live short lives because they are fabulously profligate with their (greater) resources. Similarly, stars less massive than the Sun can live much longer than it because they are so faint. Below about a third the mass of the Sun, the stars remain fully convective, so they can mix their entire supply of hydrogen into the core. This means the fuel supply for a low mass star can be the same as that for the Sun (which only uses 10% of its hydrogen). Such stars can last trillions of years!

One of the best ways to test the theories of stellar evolution is to look at star clusters of different ages. Sometimes when stars form, they form in big groups which all have about the same age, are made of the same composition, and have a variety of masses. As the cluster ages, the stars will leave the main sequence according to their mass - highest mass stars first. For clusters with very high mass stars the low mass stars may not even make it to the main sequence before the first stars die. By studying the HR diagram of a cluster (a task made easier by the fact that all stars are at the same distance) we can see if our predictions of how a star evolves as a funtion of mass are borne out. By studying clusters of different ages, we can fill in the whole picture.

Star Clusters

There are 2 basic types of star clusters: open and globular. Below are some of the comparative characteristics of each:
Open clusters
    no regular shape
    relatively young (few billion years or less)
    main sequence can extend to high masses (depending on age)
    composition similar to Sun
    contains few hundred to a few thousand stars
    found in galactic plane (disk)
Globular clusters
    spherical in shape
    old stars (several billion to 12 billion years; almost age of Universe)
    main sequence cut-off at low mass stars
    few heavy elements compared to Sun
    hundred thousand to million stars
    distributed in galactic halo (spherical distribution much bigger than disk)

pictures of clusters

Because all the stars in a cluster are at the same distance, we can find that distance by "main sequence fitting". This just means that since we know the intrinsic luminosity of main sequence stars (by local calibration), we can shift the cluster apparent brightnesses to the intrinsic main sequence luminosities by adjusting the assumed distance.
The cluster age can then be found by asking how bright or hot the main sequence extends to. For a given age, all the stars whose lifetime is less than that age will have already left the main sequence. So the age of the cluster is the lifetime of stars just at the "main sequence turnoff" today. The speed with which stars evolve after they leave the main sequence will also determine how many we see at each subsequent stage; if stars pass through a given phase quickly then we will not catch many of them in the act right now.
By putting all the cluster stars on an HR diagram, we can learn a lot about how their physical characteristics are determined by mass and age. We can even test the theory for stars of different compositions by looking at clusters with different compositions. For example, stars with few metals are predicted to make a "horizontal branch" in the HR diagram during the helium burning phase. This extends at a certain luminosity to rather blue colors; stars like the Sun will stay fairly close to the red giant branch. We can see that this prediction is true through observations.