We present the first detailed assessment of the large-scale rotation of any galaxy based on full three-dimensional velocity measurements .
We do this for the Large Magellanic Cloud ( LMC ) by combining our Hubble Space Telescope average proper motion ( PM ) measurements for stars in 22 fields , with existing line-of-sight ( LOS ) velocity measurements for 6790 individual stars .
We interpret these data with a model of circular rotation in a flat disk .
The PM and LOS data paint a consistent picture of the LMC rotation , and their combination yields several new insights .
The PM data imply a stellar dynamical center that coincides with the HI dynamical center ( but offset from the photometric center ) , and a rotation curve amplitude that is consistent with that inferred from LOS velocity studies .
This resolves several puzzles posed by existing work .
The implied viewing angles of the LMC disk agree with the range of values found in the literature , but continue to indicate variations with stellar population and/or radius in the disk .
Young ( red supergiant ) stars rotate faster than old ( red and asymptotic giant branch ) stars due to asymmetric drift .
Outside the central region , the rotation curve is approximately flat out to the outermost data .
The circular velocity V _ { circ } = 91.7 \pm 18.8 { { km s ^ { -1 } } } \ > ( with the uncertainty dominated by inclination uncertainties ) is consistent with the baryonic Tully-Fisher relation , and implies an enclosed mass M ( 8.7 \ > { kpc } ) = ( 1.7 \pm 0.7 ) \times 10 ^ { 10 } \ > { M _ { \odot } } .
The virial mass is larger , depending of the full extent of the LMC ’ s dark halo .
The tidal radius is 22.3 \pm 5.2 \ > { kpc } ( 24.0 ^ { \circ } \pm 5.6 ^ { \circ } ) , if the circular velocity stays flat this far out .
Combination of the PM and LOS data yields kinematic distance estimates for the LMC , but these are not yet competitive with other methods .