Constraints on the underlying potential imposed by the set of polytropic fits like to those shown in Fig. 2. Every potential is characterized by c_p and r_sp, and the color code shows the frequency of having f ≥ 0 considering all good and fair fits (93 galaxies). The whole region of c_p > 0 is discarded, whereas c_p ≤ 0 is permitted provided r_sp ≳ r_s/2. The diagram does not change much when only good fits are considered (Relative RMS < 0.02) or when only low-mass galaxies are selected (M_⋆ ≤ 10⁷ M_⊙). The parameter r_s gives the spatial scale of the stellar light distribution. Horizontal lines defining NFW potentials (c_p = 1; solid gray line) and cored potentials (c_p = 0; dashed gray line) are included.