The origin of ultra-compact dwarfs (UCDs)--objects larger and more massive than typical globular clusters (GCs), but more compact than typical dwarf galaxies--has been hotly debated in the 15 years since their discovery. Even whether UCDs should be considered galactic in origin, or simply the most extreme GCs, is not yet settled. We present the dynamical properties of 97 spectroscopically confirmed UCDs (rh >~10 pc) and 911 GCs associated with central cD galaxy of the Virgo cluster, M87. Our UCDs, of which 89% have M_star > ~2X10^6 M_sun and 92% are as blue as the classic blue GCs, nearly triple the sample of previous confirmed Virgo UCDs, providing by far the best opportunity for studying the global dynamics of a UCD system. We found that (1) UCDs have a surface number density profile that is shallower than that of the blue GCs in the inner ~ 70 kpc and as steep as that of the red GCs at larger radii; (2) UCDs exhibit a significantly stronger rotation than the GCs, and the blue GCs seem to have a velocity field that is more consistent with that of the surrounding dwarf ellipticals than with that of UCDs; (3) UCDs have a radially increasing orbital anisotropy profile, and are tangentially-biased at radii < ~ 40 kpc and radially-biased further out. In contrast, the blue GCs become more tangentially-biased at larger radii beyond ~ 40 kpc; (4) GCs with M_star > 2X10^6 M_sun have rotational properties indistinguishable from the less massive ones, suggesting that it is the size, instead of mass, that differentiates UCDs from GCs as kinematically distinct populations. We conclude that most UCDs in M87 are not consistent with being merely the most luminous and extended examples of otherwise normal GCs. The radially-biased orbital structure of UCDs at large radii is in general agreement with the tidally threshed dwarf galaxy scenario.
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