Illustration of the determination of the PIM via gas-only hydrodynamical simulations, where we find the minimum planet-to-star mass ratio (q_g) for the formation of a pressure maximum beyond the orbit of the planet. The quantity η = −h² ∂logP∕∂logr (averaged over azimuth) is shown as a function of orbital radius r (normalized to the planet’s semi-major axis a). Each curve is for a pair {q_g, h} at α = 5 × 10⁻⁴. The shaded black area shows where η ≈ 0 for the practical determination of q_g.