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Is there enough hydrogen left after a star dies so another star will have enough to light up?

A star consumes quite a lot of hydrogen in its life, and is pretty much "vacuuming" everything in its vicinity. After it dies (eventually by supernova which will spread all its composition over light ...
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Black dwarf binary systems

I know black dwarf stars do not exist yet, and that they are what white dwarfs end up after a long time. The question is really simple: would it be possible to have a binary system in which one of the ...