We present ultraviolet (UV) photometry of M31 globular clusters (GCs) found in 23 Galaxy Evolution Explorer (GALEX) images covering the entirety of M31. We detect 485 and 273 GCs (and GC candidates) in the near-ultraviolet (NUV; 2267 A) and far-ultraviolet (FUV; 1516 A), respectively. Comparing M31 data with those of Galactic GCs in the UV with the aid of population models, we find that the age ranges of old GCs in M31 and the Galactic halo are similar. Three metal-rich ([Fe/H]>-1) GCs in M31 produce significant FUV flux making their FUV-V colors unusually blue for their metallicities. These are thought to be analogs of the two peculiar Galactic GCs NGC 6388 and NGC 6441 with extended blue HB stars. Based on the models incorporating helium enriched subpopulations in addition to the majority of the population that have a normal helium abundance, we suggest that even small fraction of super-helium-rich subpopulations in GCs can reproduce the observed UV bright metal-rich GCs. Young clusters in M31 show distinct UV and optical properties from GCs in Milky Way. Population models indicate that their typical age is less than ~ 2 Gyrs. A large fraction of young GCs have the kinematics of the thin, rapidly rotating disk component. However, a subset of the old GCs also shares the thin-disk kinematics of the younger clusters. The existence of young GCs on the outskirts of M31 disk suggests the occurrence of a significant recent star formation in the thin-disk of M31. Old thin-disk GCs may set constraints on the epoch of early formation of the M31 thin-disk. We detect 12 (10) intermediate-age GC candidates in NUV (FUV). We suggest that some of spectroscopically identified intermediate-age GCs may not be truly intermediate in age, but rather older GCs that possess developed HB.
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