The fundamental property of a sunspot is that it has a strong (3 kG) magnetic field emerging largely vertically from the solar interior into the atmosphere (Hale 1908). The magnetic field of a spot is confined by the external pressure of the field-free surroundings. Magnetic fields produce a mechanical force on the conducting medium (plasma) within which they are embedded. Thus the spot's magnetic field provides a magnetic pressure which acts in combination with the plasma (or gas) pressure force within the spot; in equilibrium, these two pressure forces add together to achieve a balance with the pressure of the non-magnetic surroundings.
The Wilson Depression
Consequently, there is a gas pressure deficit in the sunspot simply because of the presence of the magnetic field. The other defining property of a sunspot is its reduced temperature, which also acts to reduce the gas pressure with the spot. The result is that the central region of a sunspot - the umbra - is lower in pressure, density and temperature than the surrounding penumbra and the field-free plasma of the environment.
The spot has the appearance of a funnel, with the umbra occupying the central region being a region of lower pressure, density and temperature. This is manifest as the Wilson Depression, discovered in 1769, whereby the penumbra of a spot observed on the solar limb appears broader on the side near the limb than on the side furthest from the limb. The umbra has sunk down within the spot. The extent of the depression is not easy to determine and no doubt varies from spot to spot, but it is of order 500 -700 km, and so is small compared with the overall extent (104 km) of a typical sunspot.
Article by: Bernie Roberts, University of St Andrews