Time over semimajor axis evolution of the N-body simulation in LIPAD. The time and location at which an object has first reached lunar mass is indicated by the black dots in the plot. The subsequent growth of the embryo is tracked and connected with the gray lines (its mass is given by the color bar). The mass after one million years in planetesimals is 13 M_⊕ in these runs. The planetesimal surface density slope is varied (Σ_P ∝ r^−1.0, Σ_P ∝ r^−1.5, and Σ_P∝ r^−2.0 ). The red line indicates where M_prot surpasses the mass of a lunar-mass planetary embryo in the analytical model from Sect. 2.2, assuming the same evolution of the planetesimal surface density that is given to the N-body simulation.