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 vt, 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 vt, 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 vt by compiling and improving LMC proper-motion measurements from the literature, and we show that for known vt, all other model parameters are uniquely determined by the data. The position angle of the line of nodes is Θ = 1299 ± 60, 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 = -103° ± 61° 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 ± 15.9 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 σ = 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 12 ± 06 from the kinematic center of the H I. The enclosed mass inside the last data point is MLMC(8.9 kpc) = (8.7 ± 4.3) × 109 M⊙, more than half of which is due to a dark halo. The LMC has a considerable vertical thickness; its V/σ = 2.9 ± 0.9 is less than the value for the Milky Way's thick disk (V/σ ≈ 3.9). Simple arguments for models stratified on spheroids indicate that the (out of plane) axial ratio could be ~0.3 or larger. Isothermal disk models for the observed velocity dispersion profile 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 rt = 15.0 ± 4.5 kpc (i.e., 171 ± 51). 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 σ. The compiled proper-motion data imply an LMC transverse velocity vt = 406 km s-1 in the direction of position angle 787 (with errors of ~40 km s-1 in each coordinate). This can be combined with the observed systemic line-of-sight velocity, vsys = 262.2 ± 3.4 km s-1, to calculate the LMC velocity in the Galactocentric rest frame. This yields vLMC = 293 ± 39 km s-1, with radial and tangential components vLMC,rad = 84 ± 7 km s-1 and vLMC,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 ~2.5 : 1, a perigalactic distance ~45 kpc, and a present orbital period around the Milky Way of ~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: MMW ≥ 4.3 × 1011 M⊙ and rh ≥ 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 kinematic distance estimates for the LMC.