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Stellar evolution refers to how individual stars change as they age; the life histories of stars, if you will. As you can see, it’s a bit of a misnomer … evolution – in living things like trilobites, bacteria, and flowering plants – means how species (etc) change with time, not how individuals within a species change with time!
Of course, individual stars change extremely slowly, on human timescales (~70 years), even on human history timescales (~4,000 years), so research on stellar evolution is done by combining observations of millions (even hundreds of millions) of individual stars with models of stars, which are ‘evolved’ in computer simulations.
Stars go through several distinct stages as they evolve (age) from birth to death … and the specific stages vary according to a star’s initial mass (‘birth weight’, but of course mass is not weight). Oh, and stars which are born as close twins (close binaries) have very different lives than other stars!
Stars do not have genes, nor cells; stars rarely eat (though they do sometimes expel gas rather abruptly) … so what accounts for the changes stars undergo? Basically, all stars have a mass problem … they need something to stop them from collapsing. Most of their lives – the time they spend on the main sequence – stars keep from collapsing by being very hot in their centers … the heat is manifest as pressure, which stops contraction (and the heat is supplied by the conversion of hydrogen to helium). When the hydrogen in the core runs out, hydrogen around the core is ‘burned’ (the shell burning phase), and the star gets really bloated (the red giant stage); and then … (I’m going to skip over lots of stuff here) … eventually the star does get to shrink, dramatically, to become a white dwarf (about the size of the Earth), which can’t shrink further (because the matter it’s made of is now in a new form, not found on Earth, called electron degenerate matter), and which slowly cools …
Well, that’s the briefest of brief sketches; low mass stars don’t ever become red giants, and high mass ones go through several other stages before really going out with a (really, really big) bang. Oh, and stars in close binaries have considerably more complicated lives.
To find out more: The University of Oregon’s The Electronic Universe project has a good intro to Stellar Evolution, as does the University of California San Diego, and Chandra too; for animations of simulations, the Illinois Astrophysical Fluid Dynamics Group has a wonderful Stellar Structure and Evolution Simulator!
Given how central stellar evolution is to astrophysics, you won’t be at all surprised to learn that there are many Universe Today articles on stellar evolution; here are just a few: Supercomputer Simulates Stellar Evolution, Fine Young Big Blue Cannibal Stars, and Primordial Stars Frozen Indefinitely by Dark Matter.