We formulate a new , revised and coherent understanding of the structure and dynamics of the Large Magellanic Cloud ( LMC ) , and its orbit around and interaction with the Milky Way .
Much of our understanding of these issues hinges on studies of the LMC line-of-sight kinematics .
The observed velocity field includes contributions from the LMC rotation curve V ( R ^ { \prime } ) , the LMC transverse velocity vector { \vec { v } } _ { t } , and the rate of inclination change di / dt .
All previous studies have assumed di / dt = 0 .
We show that this is incorrect , and that combined with uncertainties in { \vec { v } } _ { t } this has led to incorrect estimates of many important structural parameters of the LMC .
We derive general expressions for the velocity field which we fit to kinematical data for 1041 carbon stars .
We calculate { \vec { v } } _ { t } by compiling and improving LMC proper motion measurements from the literature , and we show that for known { \vec { v } } _ { t } all other model parameters are uniquely determined by the data .
The position angle of the line of nodes is \Theta = 129.9 ^ { \circ } \pm 6.0 ^ { \circ } , consistent with the value determined geometrically by van der Marel & Cioni ( 2001 ) .
The rate of inclination change is di / dt = -0.37 \pm 0.22 \ > { mas } { yr } ^ { -1 } = -103 \pm 61 degrees/Gyr .
This is similar in magnitude to predictions from N -body simulations by Weinberg ( 2000 ) , which predict LMC disk precession and nutation due to Milky Way tidal torques .
The LMC rotation curve V ( R ^ { \prime } ) has amplitude 49.8 \pm 15.9 \ > { km } { s } ^ { -1 } .
This is 40 % lower than what has previously ( and incorrectly ) been inferred from studies of HI , carbon stars , and other tracers .
The line-of-sight velocity dispersion has an average value \sigma = 20.2 \pm 0.5 \ > { km } { s } ^ { -1 } , with little variation as function of radius .
The dynamical center of the carbon stars is consistent with the center of the bar and the center of the outer isophotes , but it is offset by 1.2 ^ { \circ } \pm 0.6 ^ { \circ } from the kinematical center of the HI .
The enclosed mass inside the last data point is M _ { LMC } ( 8.9 \ > { kpc } ) = ( 8.7 \pm 4.3 ) \times 10 ^ { 9 } \ > { M _ { \odot } } , more than half of which is due to a dark halo .
The LMC has a considerable vertical thickness ; its V / \sigma = 2.9 \pm 0.9 is less than the value for the Milky Way ’ s thick disk ( V / \sigma \approx 3.9 ) .
Simple arguments for models stratified on spheroids indicate that the ( out-of-plane ) axial ratio could be \sim 0.3 or larger .
Isothermal disk models for the observed velocity dispersion profile confirm the finding of Alves & Nelson ( 2000 ) that the scale height must increase with radius .
A substantial thickness for the LMC disk is consistent with the simulations of Weinberg , which predict LMC disk thickening due to Milky Way tidal forces .
These affect LMC structure even inside the LMC tidal radius , which we calculate to be r _ { t } = 15.0 \pm 4.5 \ > { kpc } ( i.e. , 17.1 ^ { \circ } \pm 5.1 ^ { \circ } ) .
The new insights into LMC structure need not significantly alter existing predictions for the LMC self-lensing optical depth , which to lowest order depends only on \sigma .
The compiled proper motion data imply an LMC transverse velocity v _ { t } = 406 \ > { km } { s } ^ { -1 } in the direction of position angle 78.7 ^ { \circ } ( with errors of \sim 40 \ > { km } { s } ^ { -1 } in each coordinate ) .
This can be combined with the observed systemic velocity , v _ { sys } = 262.2 \pm 3.4 \ > { km } { s } ^ { -1 } , to calculate the LMC velocity in the Galactocentric rest frame .
This yields v _ { LMC } = 293 \pm 39 \ > { km } { s } ^ { -1 } , with radial and tangential components v _ { LMC,rad } = 84 \pm 7 \ > { km } { s } ^ { -1 } and v _ { LMC,tan } = 281 \pm 41 \ > { km } { s } ^ { -1 } , respectively .
This is consistent with the range of velocities that has been predicted by models for the Magellanic Stream .
The implied orbit of the LMC has an apocenter to pericenter distance ratio \sim 2.5 : 1 , a perigalactic distance \sim 45 \ > { kpc } , and a present orbital period around the Milky Way \sim 1.5 \ > { Gyr } .
The constraint that the LMC is bound to the Milky Way provides a robust limit on the minimum mass and extent of the Milky Way dark halo : M _ { MW } \geq 4.3 \times 10 ^ { 11 } \ > { M _ { \odot } } and r _ { h } \geq 39 \ > { kpc } ( 68.3 % confidence ) .
Finally , we present predictions for the LMC proper motion velocity field , and we discuss how measurements of this may lead to kinematical distance estimates of the LMC .