Height dependence of the gas pressure and the magnetic pressure given in Eq. (6) in the umbra. Black curve: reference gas pressure (P_ref) in the quiet Sun, extracted from a MHD simulation, blue: gas pressure averaged over the umbra, red: magnetic pressure averaged over the umbra (), and green: inferred curvature integral (F_c/8π). The error bars are increased by a factor of 10 in the plot for better visibility.