Actually, one possibility would be....
fairë(1)
noun "phantom, disembodied spirit, when seen as a pale shape" (pl.
fairi in
Markirya); compare
ausa. The noun
fairë was also used = "spirit (in general)", as a kind of being
(MR:349, PE17:124). In VT43:37 and VT44:17,
fairë refers to the Holy Spirit (
fairë aista or
Aina Fairë)
Not surprisingly, Tolkien toyed with a lot of different meaning for the word fairë! But 'spirit' or 'ghost' does seem to be one of them
I agree that the Maiar/Valar/Ainur do not have fëar, as that word is more appropriately applied to incarnate beings (elves, men, possibly dwarves
) Tolkien did use 'fëa' at least once in reference to the Holy Spirit, but the other uses are consistent.
Not to be confused with.....
fana noun term denoting the "veils" or "raiment" in which the
Valar presented themselves to physical eyes, the bodies in which they were self-incarnated, usually in the shape of the bodies of Elves (and Men)
(RGEO:74, PE17:173-180). According to PE17:26,
fana may be said to mean “shape” with “added notion” of light and whiteness, “it is thus often used where we might use ‘a vision’ – of something beautiful or sublime”, yet with no connotation of “uncertainty or unreality”.
Fana would then be the equivalent of hroa, but for the Ainur/Valar/Maiar.