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We have OBAFGKM to denote the strength of hydrogen lines.

Apparently we added S, N, C, and the W classes when we learned of new kinds of stars.

We use T, L, and Y to denote brown dwarfs.

The D classes refer to electron-degenerate stars (white dwarfs).

I've looked around quite a bit and I haven't seen anything regarding neutron stars and black holes. Does this mean there's no common symbol or abbreviation? What do they use in star catalogs? (I've never found a catalog with stars of all degeneracies in it.)

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Neutron stars and black holes do not have assigned spectral types since they do not have a measurable optical/IR spectrum - which is the basis for assigning a spectral type.

There are many classifications for systems containing black holes and neutron stars. They are not related to the letter-based spectral types of "normal" stars or white dwarfs, but more to do with their X-ray, radio or inferred physical properties (e.g low- or high-mass X-ray binary systems).

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