The two left panels display a cut of the density of phantom dark matter around a Plummer sphere with a Plummer radius = 0.85 kpc, mass = 5.1 × 10⁷M_⊙) representing a Sgr-like progenitor at 20 kpc from the Galactic center (upper left panel) and at 80 kpc (lower left panel). The Galactic center is respectively at (X,Y) = ( − 20, 0) kpc and (–80, 0) kpc on this plot. The two right panels display the corresponding effective potential for a dwarf galaxy on a circular orbit around a 5.6 × 10¹⁰M_⊙ point mass.