PM kinematics of M31 (left) and M33 (right). All 5p and 6p sample stars with G_BP − G_RP ≤ 2.6 are marked as red dots. The blue segments represent their predicted PMs from disk rotation, as determined in Sects. 3.1.1 and 3.1.2, without considering the systemic PM component. The derived M31 and M33 COM PMs (after zero-point correction) using the 5p sample in the heliocentric frame are shown as the magenta segments at the bottomleft corner of each panel. Green segments illustrate the average observed PMs in six (four) position angle bins for M31 (M33), after zero-point correction and subtraction of the COM PM. Each bin contains more than 210 (300) sources for M31 (M33), with bin boundaries indicated by dashed black lines. In each case, the PM direction starts at the dot and points along the line segment.