tokens: every system, the highest mass is generally achieved when pebble accretion is included. While the systems in which pebble accretion is neglected fail to build super-Earths with our input parameters, the formation of such planets becomes possible when pebble accretion is included. While the number of active embryos decreases when pebble accretion is included (see Fig. 6 ), their masses increase drastically. 4.3 Active number and total mass Figure 6 shows the total number of embryos and the total mass that is in embryos over time for the setups from Figs. 2 – 4 . We also give the fraction of total embryo mass M Emb over the mass that was given to the planetesimaldisk after 1 Myr ( M D ) for each setup. The first embryos always form in the systems in which pebble accretion is enabled. However, the number of active embryos during the simulation is almost a factor of 2 below the number of embryos in the systems without pebble accretion. The mass in embryos differs even more strongly than the active number of embryos for the corresponding systems. The fraction M Emb ∕M D consistentlyincreases for higher total masses and steeper Σ P -profiles, respectively. In the systems in which pebble accretion is included, it can exceed unity. This means that the mass in planetary embryos can be higher than the mass that is transformed into planetesimals through pebble accretion. 4.4 Orbital separation In Fig. 7 we compare the mean orbital separation of embryos over time for the systems from Figs. 2 – 4 . The orbital separation is expressed in units of the embryos Hill radii. The mean orbital separation after 1 Myr converges to ≈ 10R Hill for each setup. The simulations in which pebble accretion is included show a smoother and more stable behavior over time than the systems in which pebble accretion is neglected. The explanation of these differences lies in the fact that the first embryos can start growing farther apart from each other in the runs that only consider planetesimal accretion. Therefore numerous embryos are needed in order to converge for a characteristic orbital Hill spacing. Fig. 2 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, and its mass is given by the color bar. The mass in planetesimals after 1 Myr is given by 6 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 ). Left panels : system without pebble accretion. Right panels : system in which pebble accretion is included. The red line indicates the time after which the analytic model presented in Voelkel et al. (2021) states that embryo formation is possible. Fig. 3 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
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