Top panels: density as a function of the geometrical height z (i.e., vertical coordinate) for three spatial (x, y) locations corresponding to the sunspot umbra (right), penumbra (middle), and surrounding granulation (left). These locations are indicated by white circles in Fig. 1. Bottom panels: same as top panels but for the gas pressure. Solid black curves correspond to the actual values from the three-dimensional MHD simulation (Sect. 2), whereas colored lines are the hydrostatic results using the two boundary conditions described in the text: P_hyd, 1 (red) and P_hyd, 2 (blue). The vertical dashed lines indicate the location of the z(τ_c = 1)-level (i.e., Wilson depression).