End-states (in 5 Myr) of the simulations starting with 28 embryos, each with 3 M_⊕. The simulations are separated by horizontal dashed green lines. The surviving embryos/cores are shown with filled red dots, whose size is proportional to the objects’ mass. The scale is shown in the bottom panel. The red horizontal bar shows the perihelion-aphelion excursion of these objects on their eccentric orbits. The objects beyond 15 AU are plotted for simplicity at 15.5 AU, beyond the vertical solid green line. Jupiter and Saturn are shown as blue asterisks. The label on top of each panel reports the number N of embryos and the values of f_I and f_d adopted in the simulations. (For the discussion – see Sect. 4.)

Statistical analysis of the results of the simulations starting from 28 embryos, each with 3 M_⊕. The x-axis of left plots reports the value of f_I at fixed f_d, given at the title of each plot. Similarly, the x-axis of right plots reports the value of f_d at fixed f_I. The dot, slightly displaced to the left, is the mean mass of the largest core surviving beyond Saturn, computed over the corresponding ten simulations. The thick vertical bar is the rms deviation of this quantity. The thin bar shows the excursion of the same quantity from minimum to maximum. The square in the middle and related bars are the same, but for the second-largest core. The mass scale is reported left of the diagram. The cross, slightly displaced to the right, reports the mean number of embryos/cores surviving beyond Saturn, to be read against the scale on the right hand side. Again, the thick bar is for the rms deviation and the thin bar for the minimum-maximum quantity. (For the discussion – see Sect. 4.)

Same as Fig. A.1 but for the simulations in which the planet trap was considered. The plots a)–c) show the end-states starting with initial embryo-mass of 3 M_⊕ when the turbulence is not taken into account, plots d)–f) are related to the cases with the turbulence characterized by γ = 3 × 10^-4, 1 × 10^-3, and 3 × 10^-3, respectively. At the start, ten embryos are assumed in these simulations. Plot g) shows the end-states of simulations starting with a higher total mass (15 embryos of 3 M_⊕) and plot h) does this for a larger number of initally less massive embryos (30 embryos of 1 M_⊕). (For the discussion – see Sect. 5.)

Same as Fig. A.3 but with the initial mass of each embryo of 1.5 M _⊕ . (For the discussion – see Sect. 6.1.)

Same as Fig. A.2 but with the initial mass of each embryo of 1.5 M_⊕. (For the discussion – see Sect. 6.1.)