Reconstructed two-dimensional fields of velocity (left panel) and velocity dispersion (right panel) for M31 (upper panels) and M33 (lower panels). Each cross represents the location of a detected PN and its colour indicates the value of ⟨ V ⟩ and ⟨ σ ⟩, as computed via the adaptive Gaussian kernel smoothing in that position. The spatial scale is given in arcsec. North is up; east is left. PNe in M31 that are denoted with an open circle were excluded from the analysis of the rotation curve and radial motions.