Accretion rate over time for the simulation with self-similar profile and ε₀ = 0.05. The gas accretion rate (red) decreases as the dust back-reaction damps gas velocity,and rises again after the dust is depleted. The accretion rate of H₂, He (black) is even lower, as the gas supply of the outer regions is reduced at the snow line. The accretion rate of the standard self-similar solution (dotted line) is plotted for comparison.