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Ionized hydrogen in astrophysics is indicated by the abbreviation HII or H II (pronounced "H two") if it is a positive ion (i.e., no electron). HII regions are defined by the presence of such ions, formed from the ultraviolet EMR from early stars due to recent star formation. The same radiation heats such regions to thousands of degrees.
A negative hydrogen ion (with two electrons orbiting, a hydrogen anion) can exist and does exist in space. Left alone, it can persist, but requires only a small disturbance to strip the extra electron: a nearby positive ion or a photon that needs substantially less energy than the 13.6eV that would be needed to ionize neutral atomic hydrogen.