Vertical stratification of the sound speed at the axis of the sunspot models with z_WD = 250 km (top panel), z_WD = 350 km (second panel), z_WD = 450 km (third panel), and z_WD = 550 km (bottom panel), where z is height and z = 0 is defined at the quiet-Sun photosphere. The color of the lines indicates the photospheric umbral magnetic field strength of the model: B_u = 1500 G km (black), B_u = 2500 G (blue), and B_u = 3500 G km (red). The vertical dotted lines illustrate the height where β = 1 for the model with the magnetic field associated to the corresponding color. The thick black dashed line illustrates the sound speed in the quiet Sun.