Time evolution of Z = Σ_p∕Σ_g obtained by the numerical simulation with Ṁ_g,0 = 10⁻⁷M_⊙ yr⁻¹, Ṁ_pe =10⁻⁹M_⊙ yr⁻¹, and t_diff = 10⁶ yr. The magenta, blue, and green solid lines show Z obtained at r_d,0 by the numerical results of with r_d,0 = 30, 100 and 300 au. The dashed lines indicate gradients for individual cases given by Eqs. (37) and (38), where the absolute values of Z are arbitrary.