Third-Epoch Magellanic Cloud Proper Motions II: The Large Magellanic
  Cloud Rotation Field in Three Dimensions
  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 LMC by combining our HST 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, and a rotation
curve amplitude consistent with that inferred from LOS velocity studies. The
implied disk viewing angles agree with the range of values found in the
literature, but continue to indicate variations with stellar population and/or
radius. Young (RSG) stars rotate faster than old (RGB/AGB) stars due to
asymmetric drift. Outside the central region, the circular velocity is
approximately flat at Vcirc = 91.7 +/- 18.8 km/s. This is consistent with the
baryonic Tully-Fisher relation, and implies an enclosed mass M(8.7 kpc) = (1.7
+/- 0.7) x 10^10 solar masses. The virial mass is larger and depends on the
full extent of the dark halo. The tidal radius is 22.3 +/- 5.2 kpc (24.0 +/-
5.6 degrees). Combination of the PM and LOS data yields kinematic distance
estimates for the LMC, but these are not yet competitive with other methods.
