The VMC survey -- LV. The coherent expansion of the SMC

The Small Magellanic Cloud (SMC) exhibits significant kinematic disequilibrium due to interactions with the Large Magellanic Cloud (LMC). Here, we investigate the two-dimensional stellar kinematics of the SMC to understand the dynamical effects of these interactions by exploiting the increased time baseline of 6-11 years from the VISTA Survey of the Magellanic Clouds (VMC) data release 7. We derive proper motions with a threefold improvement in precision compared to previous studies based on VMC data. We used a geometric framework accounting for perspective effects from line of sight motion to model the systemic motion across the SMC and construct a residual proper motion map. We further introduce an anisotropic linear velocity gradient model to quantify the stretching of the galaxy. For the first time across all stellar populations, the residual proper motion map reveals expansion along the south-east and north-west directions, consistent with LMC-induced tidal forces, detectable even in the central regions. The gradient-corrected residuals show predominantly radial motions towards the SMC centre with no evidence of rotation. Velocity maps for different stellar populations, without assuming a rotating-disk model, reveal a coherent northward motion away from the centre exclusively in older red giant branch stars, interpreted as a kinematic signature of a past (>2 Gyr ago) interaction. This study highlights the inadequacy of simple rotating-disk models in capturing the internal kinematics of the galaxy.