Well as an astronomy student I must say that I always cringe when I hear someone mention that stellar evolution is impossible. Even more so when I heard that the reason it is impossible is that we have never observed it directly, i.e. we have never seen a star birth or a star changing into another stars. I will start by answering this since we have never seen it directly it cannot happen and then I will talk about stellar evolution itself.
So for the sake of argument lets imagine a sentient specie of bacteria that lives on average for an hour. Meaning that for this specie that every minute is roughly the same as a year of human life. Now, in a 24 hours period 1440 years would have happened in this civilization history. Suppose that in the last 12 hours they developed optical means to see humanity. Now since one of our minute as the same meaning as a year for them and that one day is about the timescale of their current civilization humanity would look like eternal unchanging but moving object. Now this species is rather limited in its measurement capability it can only tell three things about any given human, the speed it moves with, it height and the number of wrinkle it is showing.
I will show that with only these three parameters they could get a pretty good idea of how a human evolve in his life, without ever seeing a single human evolve. The first thing they would be doing is plotting the size of the human vs. their height, now this would be a pretty annoying plot because after a while it falls back on itself and you can’t really tell anything. However if you add a third dimension to this plot, i.e. the number of wrinkle you get a three dimensional curved surfaces that actually allows you to identify ages for humans. You have the slow, tiny and without wrinkle that are young, the fast, tall and with few wrinkles, the adult and finally the slow, tall and with a lot of wrinkle, the olds. You could event identify the pregnant woman in their own particular area of the diagram, they would be tall, slow and with few wrinkles. Granted this would only give them a rough idea of the evolution of humanity still admit that with only three easily observable parameters we can get a lot of information about the evolution of a human.
How this works is quite impressive, you see the bacteria in the example cannot ever see a human evolve, even a whole civilization of the bacteria would never see a human change (at least not significatively) except for the occasional accidental death. What gives them the information about the evolution of humanity is the diversity in the humans that they can observe. They’ll see old, young, adult, and everything in between that they can characterize them with some observable parameters. In fact, give them a few more observable and they can tell a lot more about humanity.
It’s the same thing with stars, and we have a lot more then 3 observable, not to mention that the, we’ve never seen star evolve is slightly false. We know of at least 1 star that went supernova and left a nebula with a pulsar inside. So we went to a star visible in the optical wavelength, to a big explosion that shone like a galaxy for a few days to a ball of expending gas that as a lighthouse like object that is only visible in radio emission. So we have seems a star actually change shape and nature. Of course, no single person saw this change, some documented the existence of the stars, another group saw a flash of light and we are seeing the pulsar and nebula. Still our records are good enough for us to identify all those step in the process.
Now, just what do we know about stars, what kind of stars have we seen? Well first we have what we call the main sequence stars, the stars that are like the adult of the human races. We see lots and lots of those; they are stars that according to our observation burn hydrogen in their core. We’ve seen “baby stars” like the T-Taury variables, they are stars without clouds of dust and gas that we see gas actually falling toward and sometimes when density reach critical points on the stars a flash of fusion occur and it expulse a jet of matter. We’ve seeing older stars, stars that are past their prime so to speak they now burn helium and other heavy elements in their core and have bloated to unimaginable proportion. For example, Betelgeuse, the largest star we know about, it’s about 1000 time the radius of the sun, i.e. only a little something like 700 millions km, that larger then the orbit of Mars! We also know of rebellious, middle life crisis kind of stars called Wolf-Rayet stars they are massive stars with stellar wind so intense that they expulse a significant fraction of the Sun mass every year. We also know of dying stars, little slowly cooling core of highly compact matter that we call white dwarf. We call them white dwarf because those stars are so hot, they emit what can only be called white light.
Not to mention that we also see dead stars in the form of neutron stars, and the inferred black holes in binaries system. We basically have a whole picture, not only that we have pictures of families of stars with different distribution of stars that well can be explained as an evolution sequences. We can see that from the amounts of heavy elements in the stars themselves, the groups of stars showing the most massive stars on the main sequence are also those that have the most heavy element (in general there are some exception of course). Since we know that heavy elements are produced in stars, it doesn’t take that big a leap of logic to see a sequence there.
Now, we cannot observe stars evolving, except in the spectacular supernova and even then it might be years before we can see the end result. You see, the fastest evolving star we know of, should have a lifetime on the main sequence of a few millions years, that way greater then the average research grant lifetime. However, we have more then enough examples of stars in various stages of evolution to be able to get a pretty accurate picture of the sequence. Remember that we only 3 parameters about humans you can get an evolution sequence, imagine what we can do with hundreds.