What would happen if an extremely advanced race removed the metal (everything beyond H and He) from a star.
Would the star still function? Would it change in appearance or properties at all?
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Unfortunately, there is no good way to give particularly accurate comparisons to the real world with this situation. If current cosmology is even close to correct, the earliest stars in the universe (Population III stars) should have contained almost exclusively hydrogen and helium (and a teeny weeny bit of lithium.) We have yet to discover any of these stars, so it is assumed that they were quite large and exploded in massive supernovae shortly after they formed, very early in the universe's history.
The effect of removing the metals from a star would depend very much on how large that star was.
Red Dwarf: A small, relatively cool star like a red dwarf almost exclusively undergoes reactions among protons, deuterium, and helium-3 to form helium-4. Removing any metals would only make the star slightly lighter, so its core would decompress very slightly and it would become slightly cooler as a result.
Yellow Star: Stars like the sun are large and hot enough to use their metals in fusion processes, if only sparingly. If the aliens removed all of the metals from the Sun, it would lose approximately 2% of its mass and one minor branch of the stellar fusion process would disappear. If the aliens continuously removed all metals from the sun as they were formed, it would cause the sun to dim very slightly. About 15% of the fusion events that occur in the sun use one of the affected reactions, but these particular reactions are the final steps in a longer process that has already liberated a large fraction of the energy it will produce. Further, some of the material that would have reacted in these branches would be available to react in the more typical processes.
Another set of processes that I'll cover more thoroughly in the next section would disappear entirely, causing the loss of ~1% of the Sun's fusion. In short, the Sun would dim very slightly, which would not have a massive impact on us but would be measurable and would likely have small, long term consequences to the climate.
Wikipedia has a nice diagram of the processes that occur in the sun if you're curious.
Blue Stars: Hotter stars derive more of their energy from a process called the carbon-nitrogen-oxygen (CNO) cycle, which is more strongly temperature dependent than the proton-proton cycle. The CNO cycle relies on the presence of carbon-12 to act as a catalyst for the fusion of protons into helium (via nitrogen and oxygen.) The two processes are largely independent of one another, so ending the CNO cycle would not free up additional material to react in the proton-proton cycle. Thus, if all of the metals were removed from a large, hot star, its energy production would drop dramatically. A star like Sirius derives nearly all of its energy from the CNO cycle, so it would see an enormous decrease in heat production in its core.
Once the carbon-12 was removed it is likely that it would be replenished after a (long) time via the triple alpha process unless the aliens continuously removed all of the metals from the star. This process is extremely slow in normal stars, but in the weird high density conditions that would exist here it might be more prevalent.
Other comments: The core of any star is utterly opaque to electromagnetic radiation, so any change in heat production would not be observed as a change in brightness immediately. It takes about 100,000 years for the energy of any given fusion event to escape the Sun, for example. Instead the balance between thermal energy and gravitational contraction would be upset, and a large star would contract significantly. The proton-proton cycle is linearly dependent on density, so its frequency would increase as the star's core contracted. Eventually a new stable state would form, with the star smaller, cooler, and denser than it previously was.