The VMC survey: LIV. The internal kinematics of the Large Magellanic Cloud with new VISTA observations

Context. The study of the internal kinematics of galaxies provides insights into their past evolution, current dynamics, and future trajectory. The Large Magellanic Cloud (LMC), as the largest and one of the nearest satellite galaxies of the Milky Way (MW), presents unique opportunities to investigate these phenomena in great detail. Aims. We aim to investigate the internal kinematics of the LMC by deriving precise stellar proper motions using data from the VISTA survey of the Magellanic Clouds system (VMC). The main objective is to refine the LMC's dynamical parameters using improved proper motion measurements exploiting the additional epochs of observations from the VMC survey. Methods. We utilised high-precision proper motion measurements from the VMC survey, leveraging an extended time baseline from approximately 2 to 10 years. This extension significantly enhanced the precision of the proper motion data, reducing uncertainties from 6 mas yr⁻¹ in prior studies using the VMC dataset to 1.5 mas yr⁻¹. Using this data, we derived geometrical and kinematic parameters, and generated velocity maps and rotation curves in the LMC disc plane and the sky plane, for both young and old stellar populations. Finally, we compared a suite of dynamical models that simulate the interaction of the LMC with the MW and Small Magellanic Cloud (SMC), against the observations. Results. The tangential rotation curve reveals an asymmetric drift between young and old stars, while the radial velocity curve for the young population shows an increasing trend within the inner bar region, suggesting non-circular orbits. The internal rotation map confirms the clockwise rotation around the dynamical centre of the LMC, which is consistent with previous predictions. A significant residual motion was detected towards the north-east of the LMC, directed away from the centre. This feature observed in the inner disc region is kinematically connected with a substructure identified in the periphery known as Eastern Substructure 1. This motion of the LMC sources suggests a possible tidal influence from the MW, combined with the effects of the recent close pericentre passage of the SMC ∼150 Myr ago.