On Earth, fire needs oxygen. If space has no oxygen, how does the sun continue to burn? Thanks! :) Ω
All stars burn due to nuclear fusion. Intense pressure creates intense heat. This heat and pressure drives the reaction.
Used here, the word "burn" is colloquial, not scientific.
The cool thing is that the sun doesn't really "burn" like fire does!
You're right that fires require oxygen as a reactant, but the sun runs on nuclear fusion. Nuclear fusion is the joining of atomic nuclei together and it's possible because of the high temperature and pressure in the sun's core. In the core, hydrogen nuclei fuse with other hydrogen nuclei to form helium (and this can happen with heavier and heavier nuclei with even more pressure and temperature) and photons, basically.
Additionally, one of the products of stellar fusion processes is oxygen, which is then used as an intermediate(catalyst) in further production of helium nuclei(wiki: the CNO cycle).
So if one is so inclined as to call fusion "burning", then we have to admit that oxygen IS used in at least some "burning" in stars.
Only extremely massive stars can fuse oxygen. It requires a core temperature over a billion degrees. A star this massive is called a type II supernova progenitor.
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