On the difference in darkness between sunspots

The effects of the magnetic field as well as the velocity field on sunspot equilibrium are discussed. The gas pressure difference, P, between a spot and the environments in the same horizontal layer is primarily determined by the magnetic field. Using recent model atmospheres we find that P shows a maximum value, P _max, at a depth of 650 ± 150 km below the photosphere. The value of P _max suggests that the curvature of the field lines is important for the equilibrium.It appears that, at an optical depth of unity in the umbra, the density has a value close to that of the environment at the same geometric depth (see Figure 4). If such is the case the expression for the umbra temperature (Equation (15)) may be considerably simplified (Equations (17) and (18)) and compared with observations.