The hydrogen that fuels the nuclear reactions inside a star cannot last forever. Eventually, the hydrostatic equilibrium within a star is upset, and changes start to occur. How do stars die? The life expectancy of a star is determined from the very beginning by the amount of mass used to make the star. Toward the end of the life of any star, it becomes unstable, which may cause it to evolve to a Giant phase. In this time we also have pulsating stars such as Cepheids and RR Lyræ stars. More massive stars do everything more quickly, spending just a few million years on the Main Sequence before exploding dramatically in a supernova blast. A star such as the Sun is average in so many ways and will last ten billion years before its eventual demise. Red dwarf stars have potential lifetimes longer than the current age of the universe.
Even before a star shows outward signs of the end of its life, changes are definitely occurring in the interior of these stars.
Let us take a one solar-mass star such as the Sun as an example. How will it end its life? First, don't start worrying. The Sun will continue to fuse hydrogen into helium in its center for another five billion years or so. We have plenty of time before the Sun stops producing energy. But there is that helium collecting in the core, just slowly heating up due to the immense gravitational pressure.
The growing core of waste helium forces the hydrogen fusion reaction farther and farther out, closer and closer to the surface. This has a negligible effect, at first. But, eventually the burning shell of hydrogen gets too close to the surface, and the star reacts by bloating up into a Red Giant, first passing through the Subgiant phase.
After spending a billion years or so as a red giant, the helium in the core of the star will eventually ignite in an event called the helium flash, having reached the magic temperature of 100 million Kelvin.
Globular clusters show the advanced stages of evolution very well. Here is a page that gives some details.
Things rearrange themselves in side the star and it settles down to becoming a somewhat smaller star again, although not a very stable one. The star goes through a period of shell burning again, this time with a shell of hydrogen fusion, and, inside of that, a shell of helium fusion.
Finally the star sheds its outer layers out into space. This ejected material surrounds the stellar core as what's called a planetary nebula, such as the famous Ring Nebula or the Owl Nebula. Planetary nebulæ are given that name because they do look a bit like planets in the telescope, not because they have anything to do with planets. The exposed stellar core is now observed as a white dwarf.
How does the mass of the star affect the pace of evolution? Here is a nice little simulation.
Watch this video lecture.
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Updated April 15, 2010