Constraints on the underlying potential inferred from the polytropic fit of a representative galaxy. The corresponding fit is shown in Fig. 2 (first column, second row). Each potential is characterized by two parameters, as shown in Eq. (18): the inner slope, c_p, and the global spatial scale, r_sp. Red dots correspond to f < 0 and so mark unphysical potentials, whereas blue dots correspond to f ≥ 0 and so trace potentials consistent with the density profile. The parameter r_s gives the spatial scale of the stellar light distribution. The horizontal lines define NFW potentials (c_p = 1; solid gray line) and cored potentials (c_p = 0; dashed gray line).