Intrinsic luminosity density profiles (left) and logarithmic density slopes γ(r) (right) for a sequence of core–Sérsic models with increasingly smooth transitions. All models share the same structural parameters as in Fig. 1, but the transition parameter α takes the values α = 4, 2, 1, 0.5, 0.25, and 0.1, as indicated. Large values of α produce a strong peak in the intrinsic density just outside the break radius, reflecting the discontinuity in the derivative of the projected profile. As the transition becomes smoother (smaller α), this peak gradually diminishes and shifts outwards, and the region with negative logarithmic slope γ(r) shrinks. For sufficiently small α, the density profile becomes fully monotonic and physically admissible. The comparison illustrates that the transition parameter, rather than the inner or outer slopes themselves, primarily determines whether a core–Sérsic model yields a realistic three-dimensional stellar density distribution.