The VMC survey - XLVI. Stellar proper motions in the centre of the Large Magellanic Cloud

We present proper motion (PM) measurements within the central region of the Large Magellanic Cloud (LMC), using near-infrared data from the VISTA survey of the Magellanic Cloud system (VMC). This work encompasses 18 VMC tiles covering a total sky area of ~28 deg². We computed absolute stellar PMs from multiepoch observations in the K_s filter over time baselines between ~12 and 47 months. Our final catalogue contains ~6322 000 likely LMC member stars with derived PMs. We employed a simple flat-rotating disc model to analyse and interpret the PM data. We found a stellar centre of rotation ($\alpha _{0} = 79.95^{\circ }\,^{+0.22}_{-0.23}$, $\delta _0 = -69.31^{\circ }\,^{+0.12}_{-0.11}$) that is in agreement with that resulting from Hubble Space Telescope data. The inferred viewing angles of the LMC disc ($i=33.5^{\circ }\,^{+1.2}_{-1.3}$, $\Theta =129.8^{\circ }\,^{+1.9}_{-1.9}$) are in good agreement with values from the literature but suggest a higher inclination of the central parts of the LMC. Our data confirm a higher rotation amplitude for the young (≲0.5 Gyr) stars compared to the intermediate-age/old (≳1 Gyr) population, which can be explained by asymmetric drift. We constructed spatially resolved velocity maps of the intermediate-age/old and young populations. Intermediate-age/old stars follow elongated orbits parallel to the bar's major axis, providing first observational evidence for x₁ orbits within the LMC bar. In the innermost regions, the motions show more chaotic structures. Young stars show motions along a central filamentary bar structure.