How many “generations” of stars have there been since the big bang? I realize that stars are constantly being created and destroyed just like people. But it seems like I always read about star “nurseries” and clouds of interstellar material collapsing into a cluster of relatively similar stars which live roughly the same length of time. Are there any geriatric dwarf or neutron stars left over from the first generation? And how many generations do we have left before the big fizzle or crunch or whatever?
The sun is considered a 3rd generation star. The current view is that the first stars were massive and almost completely made up of hydrogen cite. Due to their size they quickly used up their fuel and “died” after about 300 million years. Now normally large stars collapse behind an event horizon so I’d like to hear from Angua or Chronos how they managed to seed the next generation of stars.
You rang? 
You’re not quite right that massive stars will collapse behind an event horizon – they will, but not immediately. Initially, provided that the star is over a given mass limit (greater than 8 times the mass of the Sun ISTR), then the star will initially go supernova – i.e. explode. The explosion throws out the outer layers of the star, which will contain the seed material for the next generation of stars. The remnant of the star left at the centre, may, if its massive enough, then collapse to a black hole.
And just because the astronomers like to confuse people, the first generation of stars is called “Population III”, the second is “Population II”, and the current one is “Population I”. The three populations are primarily distinguished by their metal content, and no Population III stars have ever been directly observed.
So we have these incredibly massive stars that burn quickly and expand. What percentage of their initial mass is going to be blown off by the collapse of the core?
And as an aside, I went looking for an older star question thread and found the Electric Sun. Fun reading early in the morning. 
Here’s an interesting article from Discover magazine on the first generation of stars: The Real Big Bang.
That depends. Its a rather complicated question to be honest. I’ve just been talking to my officemate, who’s a supernova person, and according to her, for a star that’s about 10 solar masses just prior to supernova, about 8 solar masses will be ejecta, leaving a 2 solar mass compact object. However, most of the star’s initial main sequence mass will have been lost before the supernova even happens, in the form of stellar winds etc.
Thinking of stars as being in “generations” is something of a misnomer. There are Population I stars (which are the most recent and metals-heavy), Population II start (almost completely hydrogen and helium, a fraction of a percent lithium, with an almost negligable metal content), and by recent theory Population III stars (formed right after normal matter recondensation following the Big Bang, zero metallicity). The existance of Population III stars is inferred but there is a broad consensus on it as the primary theory for producing heavier elements by nucleosynthesis.
Star production is a constant process, though; while the populations can be differentiated by their aggregate metals content (which impacts their lifestyles) it’s not as if they occur in discrete waves. There’s a lot about star formation that isn’t well understood, since it’s a process we can’t observe direclty but have to infer from bits of clues and computer models, but Population I formation is generally thought to occur in the residue of an explosion of a larger, faster burning star which blows a significant portion of its mass (including heavier elements formed by high order fusion and stellar nucleosynthesis in the case of a supernova) into a so-called planetary nebula, which then condenses to accretion disks about protostellar masses and sucks more lighweight elements from the interstellar medium. (Population II and Population III stars tend to be much larger, burn hotter and faster, and paradoxically to intuition actually fuse very little of their material, leaving plenty of hydrogen for the subsequent stars.)
Eventually, the disks combine into a larger system, or pull each other apart, or orbit away from one another and form solar systems which are presumably not terribly dissimilar from our own in the sense of having small rocky worlds, large gaseous bodies, and a cloud of lighter, small bodies making an Oort Cloud in the outer system. Recent capabilities to observe worlds in other systems have tended to confirm the banality of the Solar System, though we found some suprising developments like close orbiting gas giants and very large rocky worlds. This too, is largely inference, so it’s possible that there are systems far stranger than we imagine.
Stranger
It’s worth noting here that “metals”, in this context, refers to any element heavier than helium. To an astronomer, carbon and oxygen are metals.
And the numbering of the populations wasn’t done intentionally to be confusing, but is a historical artifact from their discovery. Our Sun and other stars like it were the first stars studied in detail, so they ended up with the Population I label, while the later-discovered stars with different properties were called Population II. At first, it wasn’t even known that the differences were due to metallicity, it was just known that (for instance) Pop II Cepheids had a different period-luminosity relationship than Pop I Cepheids.
If a Gen II or III star passes through an interstellar nebula created by previous supernovae, wouldn’t it become enriched with metals from the nebula material? Might this give it a higher metal content than its “generation” would normally merit and result in a misclassification?
In an amazing coincidence, my computer is playing Nat King Cole singing “Stardust” as I type this.
Population II and III stars tend to be larger and undergo fusion faster, blowing away most of their mass in brilliant helium flashes and supernovae. There are no Population III stars in the visible universe (or at least not as far as we can distinguish) and they’d have lifetimes ranging from the hundreds of thousands to single millions of years. There are Population II stars still wondering around, but the likelyhood of them accreting enough from the stellar medium, even if passing through a planetary nebula, is low because of the relative velocities; however, plenty of stars in binary or larger systems accrete material from their partners (though it’s usually a dwarf star or pulsars pulling material from a blowsy giant) which can cause characteristic changes in luminosity.
Understand that these cateogories are ad-hoc attempts to classify stars; we’d regard a metal-rich star to be Population I even if it were much older by virtue of its metallicity. There are Population II stars in the Milky Way’s globular clusters that are probably younger than Population I stars in the main galactic disk just because the clusters are inately metals-poor (less material, fewer supernovae, less differential velocity to smear stuff out). And despite elaborate diagrams and computer simulations of stellar and galactic evolution, most of what we know about these topics is scientific guesswork based upon clues and inference rather than direct observation. We’re pretty confident, at this point, about the overall scheme of things, but regarding the really big questions and the really nitpicky detailed ones there is still a lot that is unknown, or at least uncertain.
Stranger
According to an article in TIME a couple of months ago, astronomers have reported finding a supernova from a massive star, 150 times the Sun’s size, which may be the same size as the Population III stars. The astronomers suggest that at that size, the explosion is so violent that nothing is left of the core - the mass that isn’t turned into energy is all blown out, becoming the seeds for future stars, earths, and sentient beings staring at computer screens.