Equilibrium Dynamical Models in the Inner Region of the Large Magellanic Cloud Based on Gaia DR3 Kinematics

We use Gaia DR3 to explore how well equilibrium dynamical models based on the Jeans equations and the Schwarzschild orbit superposition method are able to describe LMC's 5-dimensional phase-space distribution and line-of-sight (LOS) velocity distribution, respectively. In the latter model we incorporate a triaxial bar component and derive LMC's bar pattern speed. We fit Jeans dynamical models to all Gaia DR3 stars with proper motion and LOS velocity measurements found in the VMC VISTA survey of the LMC using a discrete maximum likelihood approach. These models are very efficient at discriminating genuine LMC member stars from Milky Way foreground stars and background galaxies. They constrain the shape, orientation, and enclosed mass of the galaxy under the assumption for axisymmetry. We use the Jeans model results as a stepping stone to more complex 2-component Schwarzschild models, which include an axisymmetric disc and a co-centric triaxial bar, which we fit to the LMC Gaia DR3 LOS velocity field, using a chi^2 minimisation approach. The Jeans models describe well the rotation and velocity dispersion of the LMC disc and we find an inclination angle 25.5 deg, line of nodes orientation 124 deg, and an intrinsic thickness of the disc 0.23 (minor to major axis ratio). However, bound to axisymmetry, these models fail to properly describe the kinematics in the central region of the galaxy, dominated by the bar. We use the derived disc orientation and the Gaia DR3 density image of the LMC to obtain the intrinsic shape of the bar. Using these two components as an input to our Schwarzschild models, we perform orbit integration and weighting in a rotating reference frame fixed to the bar, deriving an independent measurement of the LMC bar pattern speed 11+/-4 km/s/kpc. Both the Jeans and Schwarzschild models predict the same enclosed mass distribution within a radius of 6.2 kpc of 1.4e10 Msun.