Azimuthally averaged intensity, I/I_qs, (solid lines) as a function of radius in Mm and fraction of the spot radius. The colours indicate the simulations listed in the inset legend. For the older runs (with names ending in ‘o’ in red), the bolometric intensity is shown, and for the other runs (blue), the continuum intensity is shown. Vertical dashed lines show the position of the umbral (left panel with R < 10 Mm, right panel R < 1) and spot boundaries (left panel R > 10 Mm, right panel R = 1 black). The horizontal dashed lines in the right panel show the average umbral intensity. Values corresponding to the location of the vertical dashed lines are given in Table 2, columns r_u, r_s, r_u/s.