Properties of the average emergence at 20° latitude (λ) measured in the ASH simulation. The left panels (A) show the average radial magnetic field at the outer boundary associated with 12 000 emergence events (3000 from each of the four subsamples covering the simulation). All events were shifted in time and longitude to be centered at t = 0 and ϕ = 0. Column (B) shows the rate at which toroidal flux diffuses through the outer boundary. Column (C) shows U_ϕ, and column (D) shows U_θ. The effects of differential rotation were removed in all cases by rotating each latitude according to its local rotation rate. The black boxes are centered on the emergence location. Quantities involving U_r are not shown because U_r = 0 on the outer boundary of the simulation. Panels E to H show insets of the same quantities at one day.