Phase space diagram (V_LOS − V_sys) versus R_proj. Here, V_sys is the systemic velocity of M31 equal to −300 kms⁻¹ (Watkins et al. 2013), and R_proj is the projected linear distance in kiloparsecs to the centre of the simulated M31 remnant for the modelled stars in the GSS. The four panels show the projected phase space for each GSS-component ([1] to [4]; see Figure 6) identified by DBSCAN. All the stellar particles are colour-coded by their metallicity. All simulated particles [left column], main progenitor particles [middle column], and secondary progenitor particles [right column] are separately illustrated. Ridges from the main progenitor are marked with orange-dashed lines while those from the secondary are marked with black-dotted lines. When the same morphological feature is identified in both progenitors, then it is marked by red-dashed lines in both panels. In the leftmost panel of the GSS-component [4] row, the grey circles are simulated stars from the satellite’s trailing tail, reproduced from Kirihara et al. (2017).