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We have the "normal" main sequence stars, OBAFGKM. Below K and M are the brown dwarfs, L,T, and Y. Zooming into the area at the edges of M and L, we have spectral types M9, M9.5, L0, and L1. So I am wondering, is there any red dwarf that has a spectral type of L?

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Yes. Stars (those objects that are supported by hydrogen fusion) can be as cool as spectral type L2.

Brown dwarfs can be as warm as M4/5 when they are young.

i.e. there isn't a clear spectral type Vs mass relationship. It depends on age too.

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