Radial profiles for the model with Ṁ_start = 1.0 × 10⁻⁸ M_⊙ yr⁻¹ at the starting point of the simulation, t₀ = 2 Myr (left column), as well as at 5.0 Myr (center column) and 8.0 Myr (right column). The solid (dashed) lines correspond to a metallicity of Z = 1 Z_⊙ (Z = 0.2 Z_⊙). Panel (a) shows the disk surface density, Σ, panel (b) the disk midplane temperature, T_disk, panel (c) the optical depth, τ, and panel (d) the mass flux Ṁ_flux. The thin vertical lines in panel (a) indicate the respective position of r_c. The horizontal lines in panel (b) indicate the ambient temperature T_amb = 20 K. The horizontal dashed lines in panel (c) symbolize τ = 1, dividing optically thin regions (τ ≪ 1) from optically thick regions (τ ≫ 1).