Trends in the critical metal mass as a function of distance. The different lines correspond to a variation in solids accretion rates: 10⁻⁷ M_⊕ yr⁻¹ (dotted), 10⁻⁶ M_⊕ yr⁻¹ (dashed), 10⁻⁵ M_⊕ yr⁻¹ (solid), with proportional gas accretion Ṁ_xy∕Ṁ_peb = 5 and the remaining parameters set by Table 1. Planets with grain-free envelopes (gray lines) exhibit a downward trend with orbital separation because the molecular opacity scales positively with temperature. The opacity generated by pebbles and dust (black lines) increases the critical mass significantly in the outer disk, especially at higher accretion rates.