Ratio between radii characterizing the effect of the expansion of the DM halo on an initially isotropic stellar velocity distribution. It shows final core radius ratio ⋆ r_c/DM r_c (the solid lines), the final over initial core ratio of DM (the driving expansion rate, given by the dashed lines), and the final over initial core ratio of the stars (the resulting stellar expansion rate, given by the dotted lines). They are presented versus the variation of the polytropic index (the blue lines), the cutoff radius of the initial stellar distribution (the orange lines), the initial core radius of DM (the green lines), and the initial core radius of DM but assuming circular orbits (Sect. 2.1; the red lines). The gravitational potential is an Henon’s isochrone, and the varying parameter has been normalized as explained in the caption of Fig. 4.