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First, strictly speaking a neutron star is not a nucleus since it is bound together by gravity rather than the strong force. Measuring a surface temperature for any star is deceptively simple. All that is needed is a spectrum, which gives the luminous flux (or similar quantity) as a function of photon wavelength. There will be a broad thermal peak somewhere ...


I think, honestly, it would look like a glass ball or a concave mirror with flashes of light where matter gets sucked in. A neutron star would have significant gravitational lensing. I don't think the surface itself would reflect any light, even though it's guaranteed to be the smoothest surface imaginable.


Let me add something to the second part of the question. The evidence for the existence of a black hole starts with the observation that there is a very compact, massive object that is not emitting as much light as a "normal" star of that mass. This in itself does not rule out a neutron star, because it may well be as the OP proposes that the neutron star ...


The upper mass limit for a quark star depends on your assumptions and ranges between 1 and 2 solar masses (cf. this paper (arXiv link) from 2001). It seems to me that the reason for the similarity to neutron stars' mass range is that it both compact objects satisfy the TOV equation, $$ \frac{dp}{dr}=-\frac{G}{r^2}\left[\rho+\frac{p}{c^2}\right]\left[M+4\pi ...

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