Distribution of angular momentum L_⊥ and L_z (top panel) energy E and L_z (bottom panel). The black dots show all of the stars of our sample of kinematically selected halo stars located within 2.5 kpc from the Sun. Core members from Sect. 3.1 of the Helmi streams are shown with green symbols to guide the reader’s eyes. With red, dashed lines we indicate the limits we apply to select additional members of the Helmi streams. In the background, the location of the disc(s) is shown with a grey density map.