Distance distribution of selected BHB stars through a succession of increasingly restrictive kinematic selections. Panel a: distance distribution of BHB stars prior to any kinematic selections, where the orange stars show the positions of the 56 spectroscopic stars whose orbits have been used to define the orbital plane of the Cetus stream. Panel b: same distribution for stars after a first broad kinematic cut performed in the corrected proper motion, illustrated by the black lines in panel e, where the blue lines show the orbits of the spectroscopic stars used to define this cut. Panel c: distance distribution of BHB stars after an additional wide selection based on their non-corrected proper motions, as shown in panel f (see Sect. 4.2.1). Panel d: distribution of the BHBs of the Cetus stream (in purple) after two additional more restrictive selections to remove the contamination of foreground and background stars performed in the non-corrected proper motion space shown in panel g and in the position-corrected parallel proper motion space shown in panel h. In all panels, ϕ₁ and ϕ₂ refer to the ‘natural’ coordinates of the Cetus stream (see Sect. 4.1).