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Quasi-stars, if they ever existed, were stupid big and stupid bright; many times bigger, brighter, and more massive than any star supported by fusion can be. There's no question that it could be seen with the naked eye, but could our telescopes get detailed images of its surface?

As a side note, what effects would relpacing Proxima Centauri with a quasi-star have on our solar system, if any? Would it be like a second sun?

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    $\begingroup$ Given the same telescopes, you'd get the same sort of image resolution. We can't see details on Proxima or (Alpha Centauri A & B) so any details would have to be bigger than those stars. I guess the answer to this depends on the scale of structures on the surface of a quasi-star. $\endgroup$ Sep 3 at 14:45
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A quick calculation tells us that a quasi-star with a radius of 10 billion kilometers (a figure suggested by the Wikipedia page) at 4.25 lyr (Proxima's distance from the Sun) would have an angular diameter of 1.7 arcmin, which is about three times Jupiter's.

comparison of the sizes

As a comparison, here from left to right there are the apparent sizes of the Sun, the quasi-star and Jupiter. Since we are able to take exceptionally detailed images of Jupiter, even from the ground, then we would definitely be able to study the surface of the quasi star in detail.

jupiter

As for the last question, yes, it would be like a second Sun. A star with that radius, and a temperature of 10000 K (from Wikipedia) would have an apparent magnitude of -23, while the Sun has a magnitude of -26.7.

Most of the quasi-star's light would be in the UV, and so it would be blocked by the atmosphere, but it would emit in the visible enough to lighten up the night.

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