Cumulative mass of drifting pebbles crossing 50 AU and 100 AU according to different analytical models and according to the numerical simulation from Appelgren et al. (2023). In the analytical models shown here, we assume that pebbles have grown to completion and started drifting at t₀ = 0.2 Myr and that the initial metallicity is Z₀ = 0.008. Assuming constant Z over time (blue line) significantly overestimates the crossing mass compared to the simulation (black line). In contrast, the cumulative masses from the new analytical models (red and yellow lines) approach the simulated case. We note that at 50 AU, the cumulative masses from these analytical models are slightly underestimated when comparing to the simulated case since Z₀(50 AU) > 0.008 in the simulation.