On the possibility of constructing a radiative sunspot model in magnetohydrostatic equilibrium.

It is currently believed that it is impossible to construct a radiative sunspot model in magnetohydrostatic equilibrium unless magnetic fields below the surface are excessively large (greater than 100 kG). This belief is based on results obtained using the mixing length theory of convection. We wish to point out that by using a different theory of convection, due to Opik (1950), it is possible to compute a radiative sunspot model in which the field becomes no greater than 9000 G. By applying two boundary conditions (depth of spot equals depth of convection zone, and magnetic field has zero gradient at the base of the spot) we show that a radiative spot has a unique effective temperature for a given Wilson depression.