New understanding of Large Magellanic Cloud structure, dynamics, and orbit from carbon star kinematics

We formulate a new 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'), the LMC transverse velocity vector 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 v(t), this has led to incorrect estimates of many important structural parameters of the LMC. We derive general expressions for the velocity field that we fit to kinematic data for 1041 carbon stars. We calculate v(t) by compiling and improving LMC proper-motion measurements from the literature, and we show that for known v(t), all other model parameters are uniquely determined by the data. The position angle of the line of nodes is Theta=129.9degrees+/-6.0degrees, consistent with the value determined geometrically by van der Marel & Cioni in 2001. The rate of inclination change is di/dt=-0.37+/-0.22 mas yr(-1)=-103degrees+/-61degrees Gyr(-1). This is similar in magnitude to predictions from N-body simulations by M. Weinberg, which predict LMC disk precession and nutation due to Milky Way tidal torques. The LMC rotation curve V(R') has amplitude 49.8+/-015.9 km s(-1). This is 40% lower than what has previously (and incorrectly) been inferred from studies of H I carbon stars, and other tracers. The line-of-sight velocity dispersion has an average value sigma=20.2+/-0.5 km s(-1), with little variation as a 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 1.2degrees+/-0.6degrees from the kinematic center of the H I. The enclosed mass inside the last data point is M-LMC (8.9 kpc)=(8.7+/-4.3)x10(9) M-circle dot, more than half of which is due to a dark halo. The LMC has a considerable vertical thickness; its V/sigma=2.9+/-0.9 is less than the value for the Milky Way's thick disk (V/sigmaapproximate to3.9). Simple arguments for models stratified on spheroids indicate that the (out of plane) axial ratio could be similar to0.3 or larger. Isothermal disk models for the observed velocity dispersion pro le confirm the finding of Alves & Nelson that the scale height must increase with radius. A substantial thickness to 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's tidal radius, which we calculate to be r(t)=15.0+/-4.5 kpc (i.e., 17.1degrees+/-5.1degrees). The new insights into LMC structure need not significantly alter existing predictions for the LMC's 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 78.7degrees (with errors of similar to40 km s(-1) in each coordinate). This can be combined with the observed systemic line-of-sight velocity, v(sys)=262.2+/-3.4 km s(-1), to calculate the LMC velocity in the Galactocentric rest frame. This yields v(LMC)=293+/-39 km s(-1), with radial and tangential components v(LMC,rad)= 84+/-7 km s(-1) and v(LMC,tan) = 281+/-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 similar to2.5:1, a perigalactic distance similar to45 kpc, and a present orbital period around the Milky Way of similar to1.5 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(MWgreater than or equal to)4.3x10(11) M-circle dot and r(h)greater than or equal to39 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 kinematic distance estimates for the LMC.