Residual proper motion maps projected onto the sky plane. Left: Motion of SMC stars after subtraction of the bulk systemic motion (bold arrow). Right: Motion of SMC stars after subtraction of a best-fitting linear velocity gradient from the residual motion shown in the left panel. The background shows the density of probable SMC sources in the VMC–Gaia EDR3 cross-matched catalogue. The red dashed boxes indicate tiles SMC 5_4 and SMC 5_2 (left to right), and the optical centre is marked by a red cross. A reference vector at the top left indicates the velocity scale. East is to the left and north is at the top.