Diagnosis of the PM distribution of stars in the field centered on Sculptor. Panel a shows the spatial distribution of all Gaia sources (gray dots) in a 5 × 5 sq deg field of view, centered on Sculptor. Among these Gaia sources, we defined an object-sample (red dots) by selecting all sources within a circle of 0.4-deg radius and a control-sample (blue dots) by selecting all sources within an annulus from 2 to 5 deg. Panel b gives the proper motion distribution of the object-sample. Panel c provides the proper motion distribution of the control-sample. In panels b, c, and d, the black eclipse (with a major-axis radius of 2.0 mas/yr) indicates the maximal region of our proper motion selection of Sculptor member candidates. To illustrate the MW contamination inside the black ellipse, panel d shows the proper motion distribution of a sub-control-sample within an annulus from 4.0 to 4.02 deg, which covers the same sky area as the black ellipse.