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Nick
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There have been theories that our solar system has a hidden dead star (Nemesis) far beyond the Oort cloud. Such hypothesis generally assume the star is now in the form of a red or brown dwarf due to the limiting constraint that we cannot see it. And realistically, even if it were still burning it would probably be too far away to look like a "second sun" without it being too massive for normal sun's planets to be stable. More likely it would be seen as a very bright star.
But even then it would have pretty bad implications for the stability of the system's planets. That's in fact one of the things that led to the Nemesis hypothesis; apparently periodic extinction events that could be explained by periodic meteor bombardments caused by a distant massive object mucking with the orbits of comets and sending them to the inner planets.

Nick
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