Cumulative mass of planetesimals, M_pla,_tot, formed by the ND mechanism as a function of time. The thin dashed lines are analytically derived cumulative masses of planetesimals (Eq. (13)). The thick solid lines are the results of numerical simulations. Here, we sorted numerical data so that planetesimal formation starts at t = 0 kyr (i.e., the time at which ρ_d/ρ_g exceeds 1, which should depend on the parameters in the numerical simulations, is always shifted to t = 0 kyr). Left panel: dependence on Ṁ_g where Ṁ_g(= 10⁻⁷, 10⁻⁸, and 10⁻⁹ M_⊙ yr⁻¹) are a variable while the disk structure (Disk 3) and F_p/g = 0.47 are kept the same. Middle panel: dependence on disk structure and F_p/g where disk structure (Disk 1 or Disk 3; see Table 1) and F_p/g(= 0.17 or 0.47) are variables while keeping the same Ṁ_g = 10⁻⁸ M_⊙ yr⁻¹. Right panel: dependence on k_SI where k_SI = 10⁻²,10⁻³, and 10⁻⁴ while having the same disk structure (Disk 2), F_p/g = 0.47, and Ṁ_g = 10⁻⁸ M_⊙ yr⁻¹. After around ~10–100 kyr, depending on the parameters, the rate of planetesimal formation can be described by the analytical arguments (dashed lines); that is, the system reaches a steady width of the planetesimal belt (Sect. 3.6). In this study, F_p/g is kept constant (i.e., infinite solid mass budget). We note, however, that the maximum total mass of planetesimals in a real system should be regulated by the mass budget of solids (see Sect. 3.6). Here, α_acc = 10⁻² and τ_s = 0.1 are used.